Striker Doumbia struck in the 72nd and 90th minute to steal a point after Lille had taken a clear lead thanks to Moussa Sow and Benoit Pedretti, who scored either way of the interval.
In their first Champions League game since the 2006/07 season, Lille dominated and played the kind of free-flowing football that led them to the Ligue 1 title last season but they proved too shaky in the closing stages.
They will next travel to Trabzonspor, who stunned 2010 champions Inter Milan 1-0 in the San Siro, in two weeks' time.
"After our second goal we played too cautiously," midfielder Pedretti told reporters.
"We are learning, but it's a bad result. Next time we'll have to be good for 90 minutes, not just 70."
Although they were without injured centre-back Aurelien Chedjou and forward Dimitri Payet, Lille got off to a lively start with Belgian prodigy Eden Hazard proving a constant threat to the visitors' defence.
Striker Sow blew a couple of clear chances after 20 minutes when he skied a close-range attempt over the bar before missing the target after dribbling past keeper Vladimir Gabulov.
Using a cautious approach, CSKA banked on counter attacks and came close eight minutes before the break when Aleksandrs Caunas's shot from inside the box went just wide.
At the end of a sharp move Hazard was denied by Gabulov, who pulled off a great save to keep his team afloat, but he was helpless when Sow found the back of the net with a back-heel from a Pedretti cross on the stroke of half-time.
Lille continued their dominance after the interval but CSKA were dangerous on the break as a Zoran Tosic attempt smashed against Mickael Landreau's right post in the 55th minute following a quick counter attack.
Two minutes later, however, Pedretti connected with a clever pass from Florent Balmont and unleashed a shot into the top corner to double their tally.
Lille then sat back and paid the price when Ivory Coast's Doumbia overpowered defender David Rozehnal in the box before firing past Landreau in the 72nd minute.
He did it again in the last minute, bursting into the area to equalise with a powerful strike that went into Landreau's top right-hand corner.
England winger Joe Cole, on loan from Liverpool, came off the bench in the 77th minute and had a chance to hand Lille a last-gasp victory but his angled shot was perfectly blocked by Gabulov before the stunned home players left the pitch heads down.
