Harris' layup came after Taylor Dyson's 3-pointer with 1:16 left put Hartford up 76-75.
Harris took control for UMass-Lowell (5-9, 1-0 American East) in the game's final 5:48. He hit back-to-back 3s in a 39-second span, and another layup and a 3 to give the River Hawks a 74-73 lead.
After his go-ahead basket he made one of two free throws for a 78-76 lead.
Hartford (5-11, 0-1) rallied from a 39-36 first-half deficit and took a 49-42 lead on George Blagojevic's layup with 16:09 left in the game.
Tyler Livingston finished with 13 points for the River Hawks, who shot 55.4 percent from the field.
Dyson finished with 27 points shooting 9 for 14 from beyond the 3-point arc.