Cristiano Ronaldo had given the visiting Spaniards a deserved 1-0 lead after 28 minutes, taking full advantage of a CSKA defensive mix-up and beating nervous-looking goalkeeper Sergei Chepchugov with a low volley into the far corner.
It was Ronaldo's 17th goal in his 23rd Champions League game for Real and 32nd in total in Europe's premier club competition.
The nine-times European champions dominated for most of the match despite playing in sub-zero temperatures on Luzhniki's unfamiliar artificial pitch but paid dearly for their misses when Sweden midfielder Wernbloom equalised in the last minute of added time following a disputed free-kick.
"I'm disappointed with the result. We should have scored the second goal, then we would have won for sure," the outspoken Portuguese told Russian television NTV Plus.
But that free-kick near the end of the game should have been taken in the opposite direction," he added.
"I must give credit to CSKA as they fought until the end, but the referee had allowed them to play very aggressively and didn't show them any yellow cards."
CSKA's Ivory Coast striker Seydou Doumbia, who has scored five goals in five Champions League games this season, was kept off the ball for most of the match by Real's tight defence.
"We made a silly mistake in the first half and they punished us. But in the second half we had some extra attackers pushing forward and probably that was the key," said CSKA coach Leonid Slutsky.
"We only had a few chances without playing particularly well but were able to get a goal in the end.
"I think Real are still the favourites but for us anything is possible."
