Going into the match needing a win and the Lille-Trabzonspor match to end in a draw in order to qualify, the defender headed home with four minutes to go, seconds after Diego Milito had headed against the crossbar at the other end.
The Russian side took the lead five minutes after the break through Ivorian striker Seydou Doumbia, but dreams of progression appeared to have evaporated when Argentine midfielder Esteban Cambiasso equalised within a minute.
CSKA's leading scorer Doumbia said it was a magical night.
"It was unbelievable to score here," he told uefa.com. "I hadn't scored for two matches so it was a great relief. It was tough to take when they equalised but I was so happy when we scored again."
Inter coach Claudio Ranieri said he was happy with his side despite a second home defeat in five days after Saturday's league reversal against Udinese, which left them 15th in Serie A.
"It seems strange but the boys are doing well," he told Sky Sport channel.
"When you go home with a defeat it's not great, but now we have to pick ourselves up for Saturday's match against Fiorentina [at home]."
CSKA enjoyed a bright start but it was the home side who should have taken the lead on 10 minutes when a three-man break ended with a brave Vladimir Gabulov diving to cut out Diego Milito's weak cross.
With the frantic early pace resembling the end rather than the start of a match, the Russian side's defences were breached a second time two minutes later when Milito fed Yuto Nagatomo but Gabulov was again on hand to save the Japanese defender's sidefoot finish.
Inter goalkeeper Luca Castellazzi was called into action for the first time on 28 minutes, throwing himself to his left to parry Vagner Love's curling strike from distance as the visitors continued to press but with more caution.
On the stroke of half-time, Milito twice went close to breaking the deadlock, firing a fraction over with a fizzing effort from the edge of the box seconds after shooting against Gabulov's frame from another well-timed break.
