Substitute Joe Allen was Liverpool's unexpected saviour with an added-time equaliser - just when Arsenal appeared to have sent a significant message in the title race.
Raheem Sterling was denied a late penalty as Manchester City were held to a goalless draw by Everton at the Etihad Stadium.
Chelsea's search for successive Barclays Premier League wins this season goes on after James McClean's late strike earned West Brom a 2-2 draw at Stamford Bridge.
Robert Huth's late header proved enough for Leicester to beat Tottenham at White Hart Lane and draw level on points with Premier League leaders Arsenal.
Unlikely hero Paul Dummett snatched a precious point for relegation-threatened Newcastle as Manchester United twice squandered the lead to draw 3-3 at St James' Park.
Harry Kane came off the bench to rescue Tottenham and keep their FA Cup hopes alive as his late penalty earned them a replay against Leicester in a 2-2 draw at White Hart Lane.
Teenage midfielder Ruben Loftus-Cheek's first senior goal settled a niggly FA Cup third round tie as Chelsea ground past Scunthorpe 2-0 at Stamford Bridge.
Sergio Aguero scored one and set up another as Manchester City cruised into the FA Cup fourth round with a 3-0 win over Norwich.
FA Cup holders Arsenal came from behind to beat a much-changed Sunderland side in their third-round meeting at the Emirates Stadium on Saturday.
Wayne Rooney scored an injury time penalty against Sheffield United to spare Louis van Gaal's blushes and send Manchester United through to the fourth round of the FA Cup by the finest of margins.
Jurgen Klopp survived his first taste of the FA Cup as his Liverpool youngsters fought back twice to salvage a 2-2 draw at Exeter.
In-form Romelu Lukaku's 12th goal in as many matches gave Everton a deserved 2-1 victory over lacklustre Manchester City in their Capital One Cup semi-final first leg at Goodison Park.
Tottenham claimed a point thanks to Dele Alli's volley but may well feel unfortunate not to have taken three as they drew 1-1 with Everton at Goodison Park.
Chelsea recorded their first win under new manager Guus Hiddink as the Blues' resurgence under their new boss continued with a 3-0 win at Crystal Palace.
Manchester City rescued their Premier League title hopes with a late comeback in a 2-1 victory at Watford.
Arsenal laboured to victory over Newcastle to start 2016 with a win and move two points clear at the top of the Premier League.
Wayne Rooney scored a superb backheel to ease the pressure on Louis van Gaal and end Manchester United's eight-match winless run.
Liverpool reject Andy Carroll ended the Reds' recent revival as West Ham secured a deserved 2-0 win at Upton Park.
Leicester lost ground at the top of the Premier League as they began the new year with a goalless draw against 10-man Bournemouth at the King Power Stadium, with Riyad Mahrez missing from the penalty spot.
Another Mesut Ozil masterclass inspired Arsenal to a 2-0 victory over Bournemouth on Monday night and guided them to the top of the Premier League in the process.
Tottenham substitute Son Heung-min broke Watford's hearts with an injury-time winner as Spurs snatched a 2-1 win against the 10-man Hornets.
Marko Arnautovic notched a dramatic late winner from the penalty spot as Stoke beat Everton 4-3 in a thriller at Goodison Park.
Manchester United put on an improved, largely entertaining display, but they could not deliver a win against Chelsea to ease the pressure on manager Louis van Gaal.
Arsenal could have gone top of the league at Southampton but return home reeling from an embarrassing 4-0 defeat, with Cuco Martina's extraordinary half-volley inspiring another unlikely result in this topsy-turvy campaign.
Three goals in 11 first-half minutes helped Manchester City sweep aside Sunderland 4-1 at the Etihad but captain Vincent Kompany's return from injury lasted only nine minutes to take the gloss of the victory.
Liverpool striker Christian Benteke's first goal since the end of October inflicted Leicester's first defeat in three months to open up a crack in their armour, 1-0 at Anfield.
Oscar slipped to send a penalty over the crossbar and blow a vital Chelsea victory against Watford in interim manager Guus Hiddink's first match in charge.
Harry Kane became Tottenham's highest league scorer in a calendar year as his first-half double fired Spurs to a 3-0 victory over struggling Norwich.
The pressure increased on Louis van Gaal after Manchester United were beaten 2-0 at Stoke.
Manchester United have sacked Jose Mourinho after Saturday's defeat at Liverpool left the club 11 points adrift of the Premier League top four.
Substitute Xherdan Shaqiri scored twice as Liverpool cruised back to the top of the Premier League with a 3-1 win over Manchester United at Anfield.
Eden Hazard scored his first goal in more than two months to help Chelsea retain their place in the Premier League's top four with a 2-1 win at Brighton & Hove Albion.
Substitute Charlie Austin headed a late winner as Southampton beat Arsenal 3-2 to give Ralph Hasenhuttl a memorable victory in his first home game in charge.
Tottenham Hotspur substitute Christian Eriksen scored in added time as they snatched a 1-0 win over Burnley at Wembley to stay within five points of leaders Manchester City in the Premier League.
Manchester City returned to the top of the Premier League as two goals from Gabriel Jesus and another by substitute Raheem Sterling secured a 3-1 home win over Everton.
Everton's France defender Lucas Digne scored with a superb free kick deep into added time to salvage a 2-2 draw with Watford in a frenetic Premier League clash at Goodison Park on Monday.
Goals on both sides of half-time gave Chelsea a 2-0 win over Manchester City in Premier League action on Saturday night.
Tottenham Hotspur moved back into third place in the Premier League after a comfortable 2-0 victory over Leicester City at the King Power Stadium on Saturday.
Lucas Torreira scored with a bicycle kick in the 82nd minute to earn Arsenal a 1-0 win over Huddersfield Town in a scrappy Premier League game on Saturday.
Manchester United earned their first Premier League win in five games with a comfortable 4-1 victory over bottom side Fulham at Old Trafford.
Mohamed Salah scored a hat trick as Liverpool eased to a 4-0 win at Bournemouth and returned to the top of the Premier League ahead of Manchester City's trip to Chelsea on Saturday evening.
Tottenham Hotspur bounced back in emphatic fashion from their derby defeat by Arsenal at the weekend with a comfortable and efficient 3-1 win over Southampton in the Premier League on Wednesday.
Manchester United and Arsenal played to a 2-2 draw on Wednesday night that saw both sides miss on several chances take the victory.
Liverpool rallied from a goal down to beat Burnley 3-1 at Turf Moor on Wednesday to keep pace with Premier League leaders Manchester City.
Diogo Jota scored his first Premier League goal as Wolverhampton Wanderers came from behind to stun title hopefuls Chelsea 2-1 at Molineux on Wednesday.
Manchester City extended their lead at the top of the Premier League to five points with a hard-fought 2-1 win at Watford thanks to the magic of Riyad Mahrez on Tuesday.
Liverpool were drawn away to Wolverhampton Wanderers in one of two all-English Premier League matchups in the draw for the third round of the FA Cup on Monday.
Liverpool snatched a dramatic late win against Merseyside rivals thanks to a bizarre 96th minute goal from forgotten man Divock Origi.
Pierre-Emerick Aubameyang scored twice as Arsenal came from behind to beat Tottenham 4-2 in a thrilling North London derby at the Emirates.
Goals from Pedro and Ruben Loftus-Cheek at either end of the match were enough to see Chelsea past Fulham in a 2-0 win in the West London Derby.
Manchester United came from behind to draw 2-2 at Southampton, but their winless run in the Premier League stretches to three games.
Relentless Manchester City made it six Premier League wins in a row with a 3-1 victory over Bournemouth on Saturday, moving them five points clear of second-placed Liverpool at the top of the table.
Leicester City's Nampalys Mendy fired home the decisive spot kick as they beat Southampton 6-5 on penalties after a 0-0 draw on Tuesday to book a Carabao Cup quarterfinal clash with holders Manchester City.
Pierre-Emerick Aubameyang's second-half goal earned Arsenal a 2-1 victory at Bournemouth which moved them to within a point of fourth-placed Chelsea.
Tottenham ended Chelsea's unbeaten start to the season after beating them 3-1 at Wembley.
Premier League champions Manchester City cruised to a comfortable 4-0 win over West Ham United at the London Stadium on Saturday as Pep Guardiola's side remained unbeaten at the top of the table.
Liverpool maintained pressure on table-topping Manchester City with three second-half goals sealing a comfortable 3-0 victory at Watford on Saturday.
A tepid Manchester United dented their hopes of catching up with the Premier League's top four after failing to spark in a dour 0-0 home draw with 15th-placed Crystal Palace on Saturday.
Manchester City took the derby spoils with a 3-1 victory over rivals Manchester United thanks to goals from David Silva, Sergio Aguero and Ilkay Gundogan, with Anthony Martial pulling one back for the visitors.