Brian Neller went 2-for-2 from the foul line with five seconds left in regulation to force overtime for host UMBC. But, with two minutes left in overtime, Rider went on an 8-2 run and won, 73-66, on Saturday night.
Chase Plummer of the Retrievers (1-9) and Jeff Jones of the Broncs (2-10) each finished with a game-high 22 points.
Rider coach Tommy Dempsey earned his 100th win and stopped a six-game losing streak.
UMBC outscored Rider 20-6 with 10 points by Plummer, to tie the score at 60 with 47 seconds left in the second half. Jones made two foul shots with 13 seconds left to give Rider a 62-62 lead, but UMBC's Neller made two of three foul shots with 5.6 seconds left to send the game into overtime.
Rider's Jonathon Thompson made a 3-pointer to give Rider a 69-64 lead with 14 seconds left. Thompson finished with 11 points.
UMBC used a 9-0 run to cut the Broncs' lead to 43-35 with 11:22 left in regulation.
Rider led 27-22 early in the second half before outscoring UMBC 16-4, with six points each by Penn and Jones, to take a 43-26 lead with 13:27 left.
Holding an 11-9 lead, Rider went on a 12-2 run to take a 23-11 lead with 7:07 left in the first half.
Rider led 25-19 at intermission.
Bowie State 94, Mercyhurst 93: Jay Gavin scored 16 points and Darren Clark had 22, and the visiting Bulldogs (6-1) made 31 of 34 free throws to edge the Lakers (6-3) in the opening game of the Mercyhurst Invitational.
Mercyhurst extended its 37-35 halftime lead in the second half to 14, but Bowie took the lead for good at 85-84 with two minutes left on a free throw by Clark.
Salisbury 83, Elizabethtown 63: The host Sea Gulls (7-3) shot 70 percent from the field in the first half and won their third straight at home. The Blue Jays fell to 2-7.
Salisbury scored 48 points in the first half, and Chris Viqueira finished with a career-best 14 points.
Salisbury fell behind early, as Elizabethtown opened the game on a 5-0 run, but 3-pointers from Tim Harwood and Mike Maczko helped the Gulls pull within one, 7-6, and a layup by Trent Epps with 14:51 left in the opening period gave Salisbury its first lead.
Wesley 86, Washington College 72: The Wolverines (3-5) scored 44 points in the paint and 19 second-chance points to beat the host Shoremen (5-4).
Wesley held a 38-31 halftime lead after forcing 14 Washington turnovers in the first half. The Wolverines led by at least 10 points for the last 16 minutes of the contest.
Chris Douglas paced Wesley with a game-high 23 points and four steals. Douglas was 7-for-11 from the field and 9-for-12 at the free-throw line. Chris Olsen (Mount St. Joseph) had 17 points, nine rebounds, and a career-high five rebounds. Kevin Breslin scored a team-high 19 points for Washington, while Sal Schittino (Loyola) added 15 points.