Allen sat out last season with a stress fracture in his right foot. He was not used in the first two games this year.
"I just waited for my turn," said Allen, who contributed four steals and was 5-for-9 from the floor and 2-for-3 from three-point range. He also had four turnovers in 24 minutes.
"He was a little nervous in the beginning, but in the second half, he settled down," Drexel coach Bruiser Flint said. "He was a lifesaver today."
Trailing 61-59, the Quakers (1-3) had possession with 20 seconds left, but Drexel's Derrick Thomas tied up Miles Cartwright as he drove the lane, and the Dragons had the possession arrow with 1.3 seconds to go.
The Dragons, already shorthanded because 6-6 sophomore guard Damion Lee (12 points per game), was sidelined with a neck injury, lost the services of high-scoring Chris Fouch with 14:07 left in the game because of a right ankle injury. Fouch, who took a team-high 20-point average into the game, started in place of Lee.
But Allen, from New Haven., Conn., picked up the slack.
"He showed he was ready," Penn coach Jerome Allen said.
Dartaye Ruffin (15 points) and Daryl McCoy 14 rebounds) also led the Dragons.
In the first half, Penn fans unfurled a banner that sarcastically complimented the Dragons: Congratulations on the NIT! You Deserved It.
They were referring to last season, when many thought Drexel should have received an NCAA bid.
Drexel has won the last five meetings in the series, billed as the Battle for 33d Street because of the schools' proximity. Penn has a 15-9 overall lead in the rivalry.
Contact Sam Carchidi at email@example.com. Follow on Twitter @BroadStBull.