كتب : Hatem Maher
The Brazilian striker netted the winner in the 24th minute to help CSKA grab a precious victory and deny Arsenal a third successive win in the competition.
The result put CSKA on top of Group G with seven points, one ahead of second-placed Arsenal.
Porto host Hamburg in the other group match later on Tuesday.
Arsenal dominated possession in the first 20 minutes but failed to impose threat while CSKA looked dangerous on the counter attacks.
Carvalho stunned the visitors in the 24th minute when he connected with Sergei Ignashevich's short pass from a free-kick on the edge of the area to fire a powerful drive past Arsenal keeper Jens Lehmann.
He almost doubled the lead five minutes later when he unleashed a swerving shot that was tipped over the bar by Lehmann.
Arsenal look determined to equalize in the second period and came close but were denied twice by the offside flag.
Gilberto Silva's goal in the 75th minute was ruled out for offside while Thierry Henry was booked for an alleged handball although the ball hit the back of the net.
Elsewhere, Portuguese giants Porto thrashed Germany's Hamburg 4-1 at the Estadio do Dragao.
Lisandro Lopez opened the score in the 14th minute before Argentinean midfielder Lucho Gonzalez doubled the lead three minutes after the interval.
Helder Postiga added the third in the 69th minute before Lopez netted his second goal nine minutes from time.
Piotr Trochowski scored the consolation for Hamburg one minute before the final whistle.
The result put Porto in third place with four points while AEK remain bottom on just one point.