Leigh Griffiths capped his first start for Celtic since last December by scoring a brilliant free-kick as Estonian side Nomme Kalju were thrashed 5-0 in the first leg of their Champions League second-round qualifier on Wednesday.
The striker made his first competitive appearance a week ago in the 2-1 win over Sarajevo, and Griffiths vindicated Neil Lennon's decision to hand him his first start for eight months following a long spell out with depression.
Kristoffer Ajer and Ryan Christie had sent Celtic on their way to an emphatic home victory before the Scotland international found the top corner from almost 30 yards to put Celtic 3-0 in front in first-half stoppage-time.
Celtic took control from the first whistle. Jozo Simunovic had two sights of goal from early corners and the visiting goalkeeper made an unorthodox stop from Christie's swerving strike.
Odsonne Edouard twice came close and Scott Brown forced a good save before the breakthrough came in the 36th minute when Ajer headed Christie's near-post free-kick in off the bar.
Christie won a 44th-minute penalty when Reginald Mbu Alidor handled as he flicked the ball into the box, and the former Inverness man sent the keeper the wrong way.
Griffiths had a shot diverted wide before finding the top corner with a curling effort, then punching the corner flag and sinking to his knees in celebration.
The second half was a procession of Celtic chances. Christie and James Forrest both had two strikes saved and Johnston also threatened twice before Christie curled home his second from 18 yards in the 65th minute.
Johnston forced another stop and the shots continued to rain in before McGregor drilled into the bottom corner from 22 yards in the 77th minute.
Olivier Ntcham came off the bench for his first appearance of the season following his trip to the European U21 Championship finals with France, and Celtic cruised through the closing stages.
Igor Stasevich inspired BATE Borisov to a 2-1 home win over Rosenborg as he converted a fifth-minute penalty and set up Maksim Skavysh's winner early in the second half after Anders Konradsen had levelled for the visitors.
A Lasha Dvali goal followed by a Davide Lanzafame brace steered Hungarian title holders Ferencvaros to a 3-1 home win over Valetta while Billel Omrani gave CFR Cluj a 1-0 victory against Maccabi Tel Aviv.
Slovenians Maribor ground a 2-1 win over AIK Stockholm after Rok Kronaveter and Sasa Ivkovic netted for the hosts while Dundalk salvaged a 1-1 draw against Azeri visitors Qarabag thanks to a late goal from Patrick Hoban.