The Terriers (8-10, 4-3 Patriot League) never trailed but needed to hang on in the final minutes when American (11-8, 4-3) closed to within 55-52 on Jesse Reed's layup with 2:14 to play.
Eric Fanning pushed BU's lead to five on a basket with 18 seconds left and Pee Wee Gardner answered with a pair of free throws for the Eagles to make it 57-54 with 13 seconds left.
Cheddi Mosely hit a pair of free throws with eight seconds left to secure the win.
Fanning added 14 points and Justin Alston 12 for the Terriers. Hankerson surpassed the four BU players who previously shared the single-game steals record at eight.
Reed scored 15 points and Marko Vasic 14 to lead the Eagles.