The opening 20 minutes were scoreless, with RMC goalie Austin Hannaford stopping all 13 shots he faced.
The teams were even at 0-0 after 20 minutes.
Late in the second period, Austin Eastman scored for the Ridgebacks. After recording two goals and an assist against the Paladins in October, Eastman had another multi-point game on Friday.
With 20 minutes left, UOIT led RMC 1-0.
Matthew Muller scored his first of the year in the latter half of the third period to tie the game and force overtime. The tying goal was the first career U SPORTS goal for the third-year defenceman from Kingston.
The teams were tied at 1-1 after 60 minutes.
Early in the overtime period, Hannaford made a game-saving poke check. The Paladins goalie finished the game with 39 saves.
With two minutes left, Mike Robinson scored his eighth goal of the year to win the game for UOIT.
RMC plays another home game on Saturday night at 7:00 PM against the McGill Redmen (6-3-1).