Patrick Richard had 22 points for the Cowboys (21-12), who shot 36 percent from the field, compared to 53 percent for Boston College.
The Eagles grabbed control with a 29-8 surge in the first half. Gabe Moton started the spurt with a 3-pointer and Raji's layup made it 36-13 with 2:43 left.
Jackson's 3-pointer in the final seconds gave Boston College a 41-19 lead at the break.
Diego Kapelan had 12 points and Stephan Martin finished with 10 for McNeese State, which welcomed a school from the Atlantic Coast Conference to Burton Coliseum for the first time. P.J. Alawoya added nine points and 12 rebounds.
"Give Boston College due credit," Cowboys coach Dave Simmons said in a release. "They are a well-skilled basketball team. Make no mistake, they are a very good team and we wish them luck in the remainder of the NIT."
Boston College went 11 for 23 from 3-point range and outrebounded McNeese State 42-27 in front of a crowd of 5,305 -- the third-largest total for the Cowboys in Burton.
"This was a great environment," Eagles coach Steve Donahue said. "The NIT should be proud. It's a challenge to play in front of a good crowd with a lot of energy."