Ryan Anderson led the Eagles (5-5) with 23 points and a career-best 19 rebounds. The Eagles missed their initial 19 shots from 3-point range and were 2 for 22 in the game.
Hanlan had 10 points and Jackson scored eight.
Ferg Myrick led New Hampshire (4-6) with 21 points and eight boards.
Patrick Konan missed a drive in the closing seconds and front-rimmed a 3 as the horn sounded.
The Wildcats had scored the first two baskets of the overtime, pulling ahead 56-52 on Chris Pelcher's fastbreak layup.
New Hampshire made it 59-54 on Chandler Rhoads' 3-pointer from the left corner, before BC's Jackson answered with the Eagles' first 3 of the game, cutting it to 59-57 with 2:18 left.
After the teams traded misses -- including another 3 for BC -- Hanlan hit a 3 from the left wing, pushing BC ahead with 48 seconds left.
Boston College had rallied from a 13-point, second-half deficit to take a 50-49 lead on Ryan Anderson's basket with just over 2 minutes to play, but Myrick's three-point play put the Wildcats back in front with 1:58 left.
Anderson's put-back tied the game 52-all with 1:34 to go.
After a jump ball gave possession to New Hampshire, Rhoads missed a contested drive into the lane with 28 seconds left.
Joe Rahon missed a 3 as time was winding down and New Hampshire grabbed the rebound as the horn sounded, sending the game to overtime.
The Eagles were 0 for 19 on 3-point attempts in regulation.
The Wildcats led by eight at halftime, but BC made an early to run and closed it to 34-30 on KC Caudill's put-back 2 1/2 minutes into the second half.
New Hampshire then scored 13 of the next 17 points, taking a 47-34 lead on Jordon Bronner's twisting basket in the lane with just under 11 minutes to play. Myrick also scored four points during the run.
The Eagles, who had a handful of 3s roll out during their long-range shooting drought, followed with a 12-0 run to slice it to 47-46 on Rahon's free throws with 6:11 left.
After BC failed to take the lead on its next three possessions -- three missed jumpers and a free throw on the front end of a one-and-one -- Pelcher had a basket in the lane for New Hampshire, making it 49-48. It ended a 6 minute, 52 second scoreless stretch.
Hanlan had a driving basket for the Eagles before Anderson gave them their first lead since early in the opening half on a layup between two defenders with 2:13 to play.
New Hampshire, which entered leading America East in both field goal percentage defense and percentage against 3-pointers, held BC to 31-percent shooting in the first half (8 of 26) and led 31-23 at halftime.
BC was 0 for 9 on 3s in the opening half.
The Wildcats led by one, 15-14, midway through the opening half and used an 11-5 run to go ahead 26-19 on Chris Matagrano's jumper.
New Hampshire outrebounded BC 22-14 in the opening half, collecting nine at the offensive end.