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The home side took the lead in the sixth minute, courtesy of an expertly executed team move.
Just before the half-hour mark, however, Dinamo came close to an equaliser when Wilson Eduardo's fierce effort cannoned off the Celtic crossbar.
Moments later, the Hoops could have doubled the hosts' lead after goalkeeper Eduardo miskicked the ball straight to Commons, but his decision to pick out a teammate instead of going for goal came to nothing.
Wilson Eduardo had another good chance in the latter stages of the first half to put the Croatians back into the game after his vicious volley had to be expertly saved by Craig Gordon.
In the 53rd minute, Dinamo nearly scored when a quick break from a corner saw El Arbi Hillel Soudani set up the unmarked Wilson Eduardo.
Despite being one on one with Gordon, the Celtic stopper was able to push the ball behind and keep his side's lead intact.
Midway through the second half, it was Marcelo Brozovic's turn to threaten the Hoops goal, the Croatian international bending an effort into the corner from just outside the box, but Gordon was there again to thwart the shot.
Celtic kept riding their luck in the latter stages of the game, as Soudani blasted an effort wide with just seven minutes to go.
Nevertheless, the away side's profligacy meant that Ronny Deila's outfit claimed all three points.