Quinnipiac erased a late nine-point deficit, closing the second half on an 11-2 run capped by an Umar Shannon three-point play with 28 seconds left to force overtime.
Ike Azotam opened the overtime period with a jumper, and Quinnipiac scored the remainder of their points from the foul line, hitting 16 of 20 to ice the game.
The Bobcats (13-8, 8-4 Mid-American) shot 47.3 percent from the field. Shannon had 21 points and Azotam had 19.
Siena (10-13, 6-6) committed a school-record 40 fouls as six players fouled out, allowing Quinnipiac to go 47 of 65 from the free-throw line. Rob Poole scored 26 points, Brett Bisping contributed 10 and Marquis Wright had 18 with 10 assists for the Saints.