Liam Chambers put RMC in front midway through the first half.
Five minutes later, Christopher Jaggarnath scored his first of the game to bring UOIT level.
Chambers and fellow Paladin Andrew Cameron were shown yellow cards in the first half. RMC earned six in total, which is the most in a game this season.
Cameron blocked a UOIT shot on the goal-line before RMC keeper Johnathan Ardell tipped it over the bar to keep the teams even.
Jaggarnath scored his second of the match to put UOIT ahead with just under 30 minutes remaining.
A pair of free kicks late in the second half were the Paladins best opportunity to equalize, but UOIT managed to keep the ball out of the net on both occasions.
Cameron and Chambers were both given their second yellows in the final 10 minutes of the match, and will miss RMC's next game.