An early double from Moussa Dembele got Celtic off to the perfect start, which looked to have been threatened after Jozo Simunovic was given a straight red.
However, a counter attack led by James Forrest and the ensuing goal was enough to put Celtic in a comfortable position.
Alashkert didn't really threaten the strong looking 10-men Celtic side, and only strong goalkeeping denied Rodgers' men more goals.
One negative from the game was that Dembele ended the game limping off injured, which isn't a good sign for next weeks' clash with Rosenborg.
Having the three-goal cushion from the first leg, Celtic were unlikely to be threatened, but they came out fighting and secured another impressive win.