Leigh Griffiths' splendid free-kick and second-half goals from Callum McGregor and Kristoffer Ajer gave Brendan Rodgers' side a morale-boosting result ahead of this weekend's Old Firm derby with Rangers - who sealed their own progression earlier on Thursday.
The Hoops were held to a frustrating 1-1 draw in last week's trip to Lithuania but encountered few such troubles in nerveless first half.
Starting without Lyon-linked strike partner Moussa Dembele, Griffiths proved he is more than capable on his own by brilliantly curling beyond Ivan Kardum in the 27th minute for his 100th goal since joining from Wolves in 2014.
Celtic's task could should have been made easier by half-time, only for Scott Sinclair and midfielder McGregor to both waste fine opportunities to put the tie beyond doubt.
Sinclair was unable to beat Kardum at point-blank range, before McGregor finished across the face of a goal from a tight angle.
But the pair combed to atone for their errors within seven minutes of the restart, McGregor clinically picking out the bottom right corner from Sinclair's pass.
And Rodgers was able to begin planning for his reunion with Steven Gerrard when Ajer put the result beyond doubt in just after the hour mark.
The defender rose to meet Griffiths' delivery with a header that evaded the scrambling Kardum and nestled in the bottom corner as Celtic wrapped up a result that goes some way to making up for their Champions League disappointment.