Goals by Moussa Sow and Benoit Pedretti had the French champions well in control after an hour of the encounter at Stade Metropole, with their opponents looking out of sorts during a one-sided opening half.
But the Russians were a different proposition after the break, and after Doumbia reduced the deficit with his first 18 minutes from time, the Ivorian doubled his tally in the final moments to shatter the Lille faithful and seal a share of the spoils.
Neither side appeared willing to commit men forward in a cagey opening period, but the half sparked into life after 20 minutes as first Pedretti fired just over for Lille with an overhead kick, and then Sow fired just wide moments later.
Lille continued to push as the half wore on, with Franck Beria and Florent Balmont forcing Vladimir Gabulov into action in the CSKA goal, while Beria drilled over the visitors' net just after the half-hour.
Lille take lead
Eden Hazard, handed his first chance to replicate his glittering domestic form on the Champions League stage, also drew a stop from Gabulov eight minutes from the break before CSKA finally came to the party, with Aleksandrs Cauna firing just wide.
Gabulov parried again from Hazard after 44 minutes, but moments later the CSKA goalkeeper was finally beaten, although in unfortunate circumstances.
Having been forced into action once again to thwart Pedretti, Gabulov was helpless from the resulting corner when Ludovic Obraniak's centre fell to Sow, who struck the post with a low shot. David Rozehnal kept the move alive by turning the ball back into the danger area, from where Sow produced a cheeky finish to finally break the deadlock.
The second half started at a much greater tempo than the first, with CSKA in particular looking fired up after their listless display in the opening 45 minutes. Zoran Tosic served notice of the Russian side's intentions with a fierce drive in the 55th minute that produced a superb parry from Lille goalkeeper Mickael Landreau.
And two minutes later that save took on even greater significance when Lille doubled their lead. Balmont was the architect, laying the ball off for Pedretti, who produced a delightful curling effort into the top right corner.
Doumbia grabs double
The lead might have been three goals when Marko Basa brought another stop from Gabulov after 65 minutes, although CSKA were far from finished and might have got one back a minute later when Vagner Love's effort was held by Landreau.
But CSKA grabbed a lifeline after 72 minutes when Tosic crossed from the left and Doumbia was on hand to steer the ball home from six yards. The goal sent the hosts into their shells for the final stages, Hazard's weak free-kick after 84 minutes their only opening in what time remained.
And with the Lille backline rocking, the inevitable happened. Alan Dzagoev opened up the home defence with a neat flick-on from the right channel, the ball running through to Doumbia, who finished unerringly with a first-time shot to rescue an unlikely point for his team.