Trailing by five at halftime, Hartford (14-14, 7-8 America East) took lead for good with 5-0 spurt capped by Carroll's basket to make it 46-43 with 7:25 to go and then hung on down the stretch.
Kevin Little cut the gap to 60-59 with 10 second left before Yolonzo Moore II sank a pair of free throws at the other end to put Hartford back up by three. Little then trimmed it to two with a free throw but Hartford's Justin Graham went 1 of 2 from the line and Maine couldn't get off another shot before the buzzer.
Graham had 13 points and Corban Wroe 12 for Hartford.
Little finished with 22 points for Maine (3-25, 2-13), Till Gloger added 13 and Troy Reid-Knight 11.