Patrick Konan chipped in with 16 points and grabbed seven rebounds for the Wildcats in the Bracket Busters matchup.
New Hampshire never trailed and led by as much as 14, 32-18, in the first half.
Towson (1-28) cut the deficit to 37-33 in the second half, but the Wildcats used a 26-7 run to go on top 63-40 with 5:16 left to play. Myrick capped the run with a jumper.
New Hampshire (11-15) held Towson to just 2 of 17 shooting from 3-point range while the Wildcats connected on 31 percent (10 of 32) shots from deep and 18 of 25 from the charity stripe.
Robert Nwankwo led Towson with 20 points and 13 rebounds, his 13th double-double of the season.