Fernando Morientes was twice on target as Liverpool FC moved to the brink of qualification for the UEFA Champions League group stage.
The Spanish international scored a fine first-half header and then a predatory strike in the second period to give the holders control of this third qualifying round tie ahead of the Anfield return on 23 August.
Dimitrov on target
Djibril Cissé had put Liverpool ahead with his fourth goal in five European matches this summer, but after Morientes's first, the Bulgarian champions hit back with a close-range header seconds before the break from Velizar Dimitrov.
CSKA were quick and competitive while playing with three up front, while Liverpool - mindful of the fast overlapping full-backs that coach Rafael Benítez had earmarked as the danger men - had John Arne Riise and Luis García hugging the flanks.
Home pressure subsides
Despite two early chances for Cissé, the hosts responded with a neat pass from Velizar Dimitrov which sent Guillaume Zadi through. Goalkeeper José Manuel Reina opted not to dive at the forward's feet, forcing him wide and out of play. The home pressure subsided as Liverpool took charge of possession, and when the visitors finally put together a passing movement with pace, they took the lead.
Steven Gerrard received a pass from García and slipped the ball sideways for Cissé to advance into the box and rifle it into the net from a tight angle. Captain Gerrard was again the provider for the second goal when he whipped a free-kick into the CSKA area for Morientes to head a fine effort past Eugen Hmaruc.
Another Liverpool goal at this point would have ended the tie as a contest, and the visitors had wasted several good openings by the time Mourad Hidiouad got away on the left and sent in a cross which Petar Dimitrov nodded past an exposed Reina.
The holders found themselves facing fired-up opponents after the break, but finally got a third goal in the 58th minute when an excellent exchange saw the ball passed from Gerrard to Cissé, back to Gerrard and then into the feet of Morientes five metres out. The former Real Madrid CF man had the composure to turn and force the ball through Hmaruc's legs for what proved to be the night's final flourish.
Late bookings for García and Stephen Warnock preceded a fine stoppage-time save by Reina from Evgeni Yordanov which preserved the English team's two-goal advantage.