Nwakamma hit two free throws to give the lead back to the Hawks, 38-37 with 5:55 remaining, after New Hampshire had rallied from an 11-point deficit early in the second half.
Just under a minute later, two free throws by Sikma gave Hartford (15-12, 8-6) the lead for good after the Wildcats (7-18, 3-10) had regained a one-point advantage.
Nwakamma hit four free throws in the final 11 seconds to secure the victory.
Chandler Rhoads scored 16 points for New Hampshire, whose only lower output this season was a 51-40 loss to Hartford on Jan. 24
The teams combined to shoot 22 percent (11 of 50) in the first half, which ended with Hartford leading 18-12. New Hampshire made just 4 of 22 shots (18.2 percent).
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.