The Spanish champions had chances to win the game and were 47-46 in front going into the final seven minutes before CSKA went on a 14-0 run up until the closing seconds of the match to win the match.
In a battle between two Italian coached teams CSKA edged a defensive battle in the first quarter 18-15, but while the Russians then upped their offense in the second quarter, Unicaja stood still.
With guards John Robert Holden and Theodoros Papaloukas starting to dictate proceedings in the backcourt for CSKA, the Russians managed to close out the quarter on a 9-0 run to go 33-24 up at the break as they kept Malaga scoreless for the final five minutes of the half.
However, it was the ACB side that raced out of the blocks quickest in the second-half as two three pointers from Carlos Cabezas helped the Spanish start the half with a 8-0 run of their own.
Both teams then started to struggle on offense again with the lead changing hands before they went into the final quarter locked on a 44-44 scoreline.
Tension was high in the arena, but CSKA's big match experience would prove key. Marko Tusek knocked down a three to put Malaga in front after another Slovenian Matjaz Smodis had put CSKA in front, but then Unicaja froze as CSKA pulled away.
Three David Andersen jumpers, a Trajan Langdon three and another two with a bonus from Langdon saw the Russians storm away, as Malaga's panicky looking offense could produce nothing but ugly shots.
Danish international Andersen would finish with 12 points and nine rebounds for the Russians while Langdon had 13 points despite some erratic shooting all night.
Cabezas top scored for Malaga with 13 but he did not have enough help and the ACB's Euroleague hopes now rest with TAU Ceramica.