Chelsea suffered a shock 1-0 defeat to struggling West Ham United at Stamford Bridge on Saturday.
Aaron Cresswell scored the winner in the second half to condemn Chelsea to back-to-back Premier League defeats.
Chelsea remain in fourth place but Tottenham reduced the gap to seven points with a win over Bournemouth.
West Ham thought they had doubled their lead after 67 minutes through Michail Antonio but VAR disallowed the goal for handball.
The victory sees West Ham steer four points clear of the relegation places and eases pressure off manager Manuel Pellegrini.
Frank Lampard's side host Aston Villa in midweek, while West Ham visit Wolves.
"I still believe in the squad. I think we've shown some great things this season. But we played below par today. It's time for a bit of character and see our reaction for Aston Villa [on Wednesday]," Lampard told reporters.
"We did not do enough in the final third I think that's been the story in the last three games."
Before the game, Chilean Pellegrini had looked in danger of becoming the third London Premier League manager this month to lose his job after Tottenham Hotspur dismissed Mauricio Pochettino and Arsenal sacked Unai Emery.
"For me the most difficult thing this week was not about my future or about the job, it was to convince the players not to change, that we were doing the right thing," Pellegrini said.
West Ham goalkeeper David Martin, whose father played for the club, made his debut on Saturday aged 33 and was in tears at the end.
"It still doesn't feel real. I'm just pleased got through it, I didn't let anyone down and actually I enjoyed it in the end," he told the BBC.
"My dad didn't say much -- I think we were both in tears. For my dad to play for the club for 21 years and see it, and for me to make my debut, keep clean sheet and get win for the boys, it is so pleasing."