Ludogorets's striker Claudiu Keseru opened the score on the 66th minute, but CSKA's forward Fedor Chalov scored an equalizer on the 75th.
The match was held at the CSKA Arena in Moscow.
In the other match in Group H, Hungary's Ferencvaros tied game with Spain's Espanyol at 2-2.
With five group stage matches played and one remaining, Espanyol leads the group with 11 points, Ludogorets has seven, Ferencvaros has six, and CSKA is dead last with two, losing all chances to make it to the knock-out stage.