The game in the capital of Belarus ended in overtime with a score of 3:2 in favor of the Kazan club.
The pucks at the winners were thrown by Artyom Galimov, Kirill Petrov, Alexander Radulov.
Minskers scored Nick Merkley and Mark Barberio.
Ak Bars (nine points) is in second place in the Eastern Conference standings.
Dynamo (nine points) is fourth in the West.
Earlier it was reported that Ak Bars beat Torpedo in the KHL regular season match.