Milos Krasic had put CSKA ahead in the 41st minute, firing in a shot from a narrow angle on the left to beat Besiktas keeper Rustu Recber.
Bobo knocked in a cross in from close range to put the home side level in the 86th minute, but Aldonin snatched all three points for CSKA with a shot in the fifth minute of injury time.
The result put CSKA through as runners-up behind Manchester United in Group B, while Besiktas finished bottom on four points behind Wolfsburg.
The build-up to the match was overshadowed by news that CSKA defenders Sergei Ignashevich and Alexei Berezutsky were suspended over a doping offence, testing positive for a banned substance after their match away to United on November 3.
The two players, ruled out of Tuesday's game, have been provisionally suspended until the case is heard by the UEFA disciplinary committee on December 17.
Besiktas, hoping to secure a Europa League place, made a confident start to the game.
Rodrigo Tello had a good opportunity to put the Turkish champions ahead in the 12th minute, but with only CSKA keeper Igor Akinfeyev to beat he fired a shot wide of the right post.
"The Tello goal-scoring opportunity was a decisive moment, because we would have been in control if we went ahead," said Besiktas coach Mustafa Denizli.
"If you look at our campaign, we had five matches where we created chances were we could have won," Denizli said.
As the first half progressed the home side failed to capitalise on its opportunities in front of goal, with Akinfeyev saving the Besiktas efforts that were on target.
CSKA went close to doubling their lead at start of the second half after a mix-up between the Besiktas defence and Rustu, which resulted in the keeper suffering a bloodied nose but no goal for the visitors.
Besiktas exerted increasing pressure as CSKA looked to protect their lead in the final stages of the game, but Matteo Ferrari and Nihat Kahveci failed to convert.
Bobo finally found the net in the 86th minute but Aldonin's strike in the final seconds won it for CSKA.
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