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.
Gonzaga has signed California transfer Jordan Mathews to a financial aid agreement for the 2016-17 season.
Coach Gilmore on CWS win: 'It's indescribable' Coastal Carolina head coach Gary Gilmore reflects on his 21 years as head coach and is proud of how far the program has come.
Two late June events provided a great start on the 2020 class and a look at some new 2019 talent.