UMBC (6-14, 2-5 America East Conference) led by 13 with 8 minutes remaining but Hartford went on a 16-3 run to tie the game at 58-58 with 2:29 left.
After two free throws by Harris gave UMBC a 60-58 lead with 2:14 to go and a Hartford turnover, a pair of offensive rebounds by Harris allowed UMBC to run over 1 1/2 minutes off the clock.
Hartford (10-12, 4-3) didn't get the ball back until the final 20 seconds, during which they missed three shots, including what would have been a game-tying jumper at the buzzer.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.