Harris Mansell added 12 points and Novar Gadson had nine points and 14 rebounds for the Broncs (19-11, 13-6 MAAC), who advance to face second-seeded Niagara in Sunday's semifinals.
Rider blew a 14-point lead, but regained control midway through the second half on a three-point play by Thompson that made it 49-48 with 10:32 remaining.
Saint Peter's, which led 46-44 with 12:26 remaining, kept it close the rest of the way, but was unable to tie the game.
Ryan Bacon scored 18 points and grabbed 11 rebounds for the Peacocks (11-19, 8-11 MAAC), who also got 14 apiece from Wesley Jenkins and Nick Leon.
Rider jumped ahead 20-6 with a 15-2 run that included back-to-back three-point plays by Thompson before Saint Peter's cut the lead to 39-32 at halftime.