The Russians have yet to win a game in the Premier League but the point earned on Thursday night ensured that they will finish second behind Tottenham in Group K.
Ismail Isa had put the Moldovans ahead following a smart move but Alexandru Epureanu equalised from a corner to ensure Anzhi's qualification.
Sheriff showed their intent to attack from the outset and produced a fine save from Anzhi goalkeeper Mihail Kerzhakov after just two minutes as he turned Cadu's shot around the post.
The home aide came back at them and won a corner shortly after but Ewerton could only head wide as the Russians began to put their stamp on the game.
Vladimir Sobolev was next to try his luck and really should have done better as he fired an effort from 12 yards wide of Vjekoslav Tomic's left post.
Anzhi were having by far the better of it and Nikita Burmistrov curled a shot wide before Serder Serderov brought a save from Tomic as half-time approached.
Serderov then blazed over the bar but Sheriff showed they still posed a threat in stoppage-time when Kerzhakov was called upon to making a brilliant save from Ricardinho.
And it was the visitors who took the lead seven minutes after the break through Isa.
Benjamin Balima advanced own the right and produced a perfect cross for Isa who got in front of his marker and volleyed home off the far post.
The lead was to last just six minutes, though, as Epureanu brought a smart save from Tomic and then headed home from the resulting corner.
Anzhi were having some joy from set-pieces and should have gone ahead from further corners but IIya Maksimov saw his header blocked and Sobolev volleyed over the bar.
Isa threatened with another header for Sheriff but Anzhi always looked like they had another gear as they eased through.