Thompson's free throw with 3:10 remaining put the Broncs (11-9, 6-2 Metro Atlantic Athletic Conference) ahead to stay, 60-59.
Tavon Sledge's layup for Iona had tied the game 59-59, ending a stretch of 5:14 without a field goal for the Gaels (12-7, 6-2).
Iona's total matched its season low. The Gaels, who had won six straight, were averaging 82.6, third highest in Division I.
Pereira made his second straight start in place of Nurideen Lindsey, who is recovering from a concussion, and hit two 3-pointers 14 seconds apart, when Rider erased a 25-14 first-half deficit to lead 35-30 at halftime.