Chris Fouch added 16 points for the Dragons (29-6), who host Massachusetts in a quarterfinal game on Tuesday.
Johnny Moran scored 19 points to lead Northern Iowa (20-14).
Drexel led by as many as 18 in the first half before Moran's 3-pointer with 34.6 seconds left closed the margin to 61-60. Northern Iowa then fouled Givens out of a timeout and he made 1 of 2 free throws with 24.3 seconds to go.
The Panthers' Anthony James missed a driving layup at the other end and Damion Lee hit two free throws with 12.9 seconds left to make it 64-60.
Chip Rank gave the Panthers life with a 3-pointer with 6.1 seconds remaining, but Frantz Massenat made 1 of 2 free throws before Moran's last-second 3-point attempt went off the back rim.
