Villa boss Martin O'Neill handed Brad Guzan a start in goal, while Gareth Barry returned in the heart of midfield alongside Stiliyan Petrov.
The home side enjoyed the better of the opening exchanges, but were unable to forge any meaningful openings against a resolute Russian defence.
Fourteen minutes in CSKA broke the deadlock as Brazilian striker Vagner Love exchanged passes with Alan Dzagoyev and raced clear of the Villa backline to fire a low, left-foot shot past the stranded Guzan.
That setback knocked Villa out of their stride and the visitors enjoyed the upper hand for several minutes.
However, just short of the half-hour mark Ashley Young broke clear on the left, but Gabriel Agbonlahor was unable to meet the cross with an on-target header.
A few minutes later another superb Ashley Young delivery from the left was headed narrowly over the top by John Carew from eight yards out.
Soon after the restart the visitors threatened again, with a fluent attack ending with Yuri Zhirkov rifling a left-foot shot narrowly over the top from the edge of the penalty area.
Eight minutes after the interval Craig Gardner's header from an Ashley Young corner from the left flicked the top of the crossbar.
Keeper Igor Akinfeev then turned aside an Ashley Young free-kick from 25 yards, before Villa had strong appeals for a penalty waived away.
Midway through the second half Villa finally found a way through, as Ashley Young's cross from the left was returned from beyond the far post by Gardner and Carew applied the finishing touch from 12 yards.
With the game evenly poised at 1-1, both sides continued to go in search of a possible winner, with play quickly switching from end to end.
Ashley Young fired a shot a yard wide from just outside the area and then curled another narrowly over the top, but the game ended all-square.