The impressive Russian's took an early first half lead through Vagner Love, but Villa rallied in the second period and deservedly drew level when John Carew rifled home from 12 yards.
Villa created a host of chances after the break but the even scoreline sets up an intriguing encounter at the Luzhniki Stadium on 26 February.
"European games are very difficult, and we were against a great team, so we can't be disappointed," Carew told Five.
"It was a good game in the end but the away game will be more difficult, and cold, so we will have to prepare well and believe we can do it, although it would have been good to get the win today."
Villa boss Martin O'Neill was upbeat despite the draw: "They've scored the away goal and you'd think it was all doom and gloom but it's far from it.
"I thought we were terrific, although we defended poorly for Love's goal.
"I thought we deserved to win. We created a great number of chances and played with great spirit."