The Bobcats (23-8) will host the winner of the Mount St. Mary's-Robert Morris game for the tournament championship at 7 p.m. March 10.
Deontay Twyman came off the bench to score 16 points as Quinnipiac improved to 14-0 at home this season.
Jaytornah Wisseh led fourth-seeded Long Island (14-17) with 33 points. Jamal Olasawere added 13 points and 10 rebounds for the Blackbirds.
Quinnipiac trailed 10-0 in the game that had nine lead changes. But the Bobcats took the lead for good on a 3-pointer by James Feldeine with 4:17 to play and hit 16 of 17 free throws down the stretch.