The win represented Ange Postecoglou's first competitive success since his appointment in June, with strikes from Liel Abada, Kyogo Furuhashi, James Forrest and Ryan Christie putting the Hoops in firm control of the two-legged encounter.
Having suffered another Champions League mishap against Midtjylland, Celtic asserted their authority early as Abada converted on the follow-up from his initial effort to open the scoring.
Furuhashi, on his first Celtic start, doubled the visitors' lead with a delicate dink just four minutes later, but Vaclav Pilar instantly responded to halve the deficit, smashing a half-volley past debutant Joe Hart.
After the hour mark, Abada twisted and turned on the edge of the area before Jan Hanus denied him, only for Forrest to sneak in on the rebound to restore the Hoops' two-goal advantage.
Tomas Malinsky curled in a second for the hosts, but Christie added an important fourth for Celtic when he directed a diving header past Hanus in the 88th minute.
Christie's late effort means Postecoglou's men, who will no longer benefit from the away goals rule in Europe, take a two-goal lead back to Celtic Park next Thursday after hosting Dundee in the Scottish Premiership on Sunday.