The home team moved into a 2-0 lead thanks to an early Kirill Kapustin goal and an effort in the second period from veteran Yury Trubachyov.
Shane Prince quickly reduced the deficit when he completed a counter-attack.
In the final frame Mikhail Stefanovich converted a pass from Evgeny Kovyrshin to tie the game after 42 minutes.
Marc-Andre Gragnani point shot found the net via a string of deflections.The Bisons will be back in action on 5 January as they host SKA St. Petersburg at the Minsk Arena.