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.
It's about time for someone other than Duke and Kentucky to grab the top class. Could it be Shaka Smart and Texas in 2017?
Which teams have enjoyed the most NCAA tournament success since 2000? Kansas' recent run to the Elite Eight vaulted the Jayhawks up the list.
There's nowhere to go but up for the Eagles, who were winless in the ACC last season but return a slew of young players who gained valuable experience.