Jeremie Boga's 71st minute strike was enough to move the Stamford Bridge youngsters six points behind their opponents in the group stage, with two games in hand
An even contest, was swung in the Blues' favour when Anton Polyutkin was sent off eight minutes into the second half.
And the English youngsters took full advantage, when Boga popped up in the box to secure the game's only goal.
A nervy finish was ensured when Blues substitute Jordan Houghton also received his marching orders just minutes later, after picking up two yellow cards.
The win moves Dermot Drummy's side to within six points of CSKA, who top Group 3, with two games in hand.
Chelsea face a trip to Norwegian outfit Molde next, who are yet to pick up a point.