The Dragons (1-2) trailed 49-42 in the second half, but went on an 18-4 run and led 60-53 on Derrick Thomas' two free throws with 0:57 remaining.
Drexel's Frantz Massenat sank one foul shot at 0:20. Then Cartwright was tied up by Thomas while driving to the basket with 1.3 seconds left. The possession arrow belonged to Drexel.
Allen's 15 points all came after halftime. He played due to an injury to high-scoring forward Chris Fouch. Allen also made four steals.
Penn's Fran Dougherty led all scorers with 21 points, and Cartwright added 18. Drexel's Daryl McKoy had 14 of the Dragons' 35 rebounds -- seven offensive.