The west London side impressed throughout their U-19 European tournament tie at their Cobham training ground, but couldn't find a way beyond Sergey Revyakin in the Russians' goal
Dermot Drummy's men made an excellent start to the first-half by taking the lead ten minutes in through Patrick Bamford, but failed to make their dominance count as CSKA hit back with two goals of their own to go in ahead at the break.
The hosts were again the better side in the second-half, with Lucas Piazon having the best of the play, but they failed to find a way past Sergey Revyakin as the Russians claimed all three points.
Chelsea first-team sensation Eden Hazard's 19-year-old brother, Thorgan, who was signed from Lens this summer, was handed a start for the U-19 clash, with highly rated Brazilian forward Piazon and English defender Nathaniel Chaolbah also featuring for the Blues.
CSKA, who are also making their debut in the European youth tournament this season, had already beaten Molde 2-1 this term, but the man who scored their equaliser in that match, Sergey Seredin, dropped to the bench.
It was a quiet but confident start from the hosts as they dominated possession and looked to pass their way out from the back at every opportunity and subsequently, ten minutes in, Hazard had the first chance of the game.
The 19-year-old broke free of the defence on the left wing but looked to have wasted the chance with a misplaced pass inside, however, the ball was retained and the Belgian was played in once more, this time getting a shot away but narrowly missing the right-hand post, though he had the keeper beaten.
Moments later, though, Chelsea had the breakthrough. Skipper Todd Kane raced forward on the right flank before driving a low cross into the box and forward Patrick Bamford was on hand to get free of his man and poke the ball past a helpless Revyakin.
The home side dominated from then on, with Hazard and Piazon in particular impressing as they evidenced all their skills running at the CSKA defence, however they failed to create any more clear cut chances.
CSKA then had a brilliant chance to go level just before the half-hour mark. Nikolaly Dergachev was played in with a delicate ball over the top, with Nathan Ake for once unable to track his man. The forward had time to compose himself and looked to lob Chelsea keeper Mitchell Beeney as he rushed out, but failed to get the ball the correct side of the right-hand post.
Chelsea hit back with a low strike from John Swift but the Russians' keeper was equal to it. Then, the visitors pushed the home side further. They had an appeal for handball turned down by referee Rob Whitton before he again said no after Dergachev fell under a challenge from Ake.
Some sloppy passing from the Blues saw Georgy Bagdasaryan have the next chance for the visitors, his strike tipped wide by Beeney, however the keeper was helpless to deny Gela Zaseev levelling the scores after 35 minutes with a fine driven shot from range.
The equalising goal, and period of dominance that came before it, clearly gave the visitors confidence as they went ahead through Dergachev with just five minutes to go until the break. The forward had been giving the hosts' back-line problems all half and broke clear once more to meet a dangerous cross from the left with a fantastic header into the corner, giving the Blues' keeper no chance.
CSKA could have extended their lead just moments later after a mistake by Alex Davey gifted the ball to Ravil Netfullin, but the forward wasted the opportunity by shooting wide of the goal.
Following the disappointment of falling behind after their initial dominance, Chelsea managed to carve out a few chances of their own before half-time. Piazon created a yard of space for himself with some dazzling footwork, before going close with a left-footed strike. Then, Kane's deflected cross from the right-wing hit the Brazilian's knee before going just over the bar.
Lewis Baker had the final chance of the first period for the hosts, after Hazard drilled a low ball to the midfielder, but his effort was weak and easily gathered by the CSKA keeper.
Chelsea came out guns blazing for the second half as Baker whipped a delivery across the face of goal, but no blue shirt was able to connect. Then, minutes later, Piazon stung the gloves of CSKA keeper Revyakin. The Blues' pressure continued as Kane fired another testing ball into the Russians' box, this time along the ground, however the visiting defence hacked it clear once more.
With just under 20 minutes gone in the second-half and the Blues still on top, Piazon came close to pulling it back to 2-2, however his header was acrobatically and expertly tipped wide by Revyakin after Jeremie Boga's cross.
Chances were hard to come by for either side, though the hosts continued to have the better share of the ball as they continued to pass it around their Russian opponents.
Drummy's men kept on searching for an equaliser with time running out in the second half, Boga played in Bamford behind the CSKA defence but yet again the hosts were denied by the Russian stopper, who was keeping his side in front.
With five minutes remaining Chelsea were inches away from a late equaliser. Firstly a one-handed save by the Russian keeper denied Piazon a deserved goal, with the ball rippling the side netting as some Blues' players thought they had scored.
Then, Boga, who had been brilliant since coming on just after half-time, dragged a low shot just wide of the left-hand post as CSKA survived some nervy moments to hang on to all three points.