CSKA defender Vasily Berezutsky skewed the ball into his own goal shortly after the break to put the visitors ahead.
Moussa Sow sealed his team's first win in the group midway through the second half, tapping into an empty net after Joe Cole's shot hit the post.
Lille's victory meant group leaders Inter qualified for the first knockout round in February with nine points regardless of the result of their match at Trabzonspor on Tuesday, which finished 1-1.
Doumbia, who also notched up 24 goals to lead the Russian league's scoring charts this season, was serving a one-game ban after being red-carded in their previous game against Trabzonspor.
CSKA, decimated with injuries to many of their key players this season, suffered another blow on the eve of Tuesday's match when midfielder Keisuke Honda was ruled out with a knee problem.
The Japan international, who had just returned to CSKA's lineup in a league game after missing more than three months with torn ligaments in his knee, aggravated the injury in training on Monday.
Franck Beria just fired wide from a sharp angle after Gabulov blocked Sow's shot.
