Ethan Jacobs made two free throws to put Colgate up 70-67 with 1:06 left to play. Allen made a layup to cut the difference to one point and Jacobs missed a 3-point attempt to put the ball back in the Pioneers' hands with 34 seconds left.
Sacred Heart (3-3) called a timeout and Allen dunked on Phil Gaetano's inbounds pass for the difference. Gaetano had eight assists.
The Raiders led by as many as five points with 2:16 to play, but four-straight points from Sacred Heart's Cane Broome kept the Pioneers alive.
Broome finished with 21 points and Allen had 14.