Cluj's return to Glasgow did not live up to their 4-3 win in August, as Celtic defeated the Romanian champions 2-0 to move top of Group E.
Celtic gained revenge for their Champions League exit to Cluj as Neil Lennon's side got their Europa League campaign up and running with a 2-0 win over the same opponents.
Romanian champions Cluj knocked their Scottish counterparts out in Champions League qualification, with a remarkable 4-3 victory at Celtic Park seeing them progress 5-4 on aggregate.
Cluj met their match in the form of Slavia Prague in the final play-off round, dropping into Europa League Group E, winning their opening fixture against Lazio.
Their return to Glasgow was not so triumphant, however, as Odsonne Edouard and Mohamed Elyounoussi sent Celtic to the top of the group.
Celtic, who drew 1-1 with Rennes in their first outing, were swiftly out of the blocks and Edouard marked a strong start with the opener in the 20th minute.
The former Paris Saint-Germain striker scored against Cluj in the extraordinary second leg in August and proved the bane of the visitors' defence again when he headed home Boli Bolingoli-Mbombo's cross.
Fraser Forster looked to have gifted Cluj an equaliser when he parried a free-kick straight to Mario Rondon, but Kevin Boli was in an offside position as he tucked in from his team-mate's pass.
And Elyounoussi doubled Celtic's lead just before the hour, netting his first Hoops goal with a tidy finish into the bottom-right corner.
Cluj pushed back, but Forster kept them at bay with a fine save from Ciprian Deac as Celtic got a first win of the group stage.