The No. 4 seeded Blackbirds (14-16) led 60-51 with 6:12 left, before a 10-1 run by the No. 5 seeded Knights (11-20).
Terence Grier's layup tied it at 61-61 with 2:11 left, setting up Onyechi's shot.
Fairleigh Dickinson then went 0-for-7 the rest of the way.
Jamal Olasewere finished with 14 points and 15 rebounds and Michael Culpo added 15 points, all on 3s, for Long Island.
The Blackbirds will face No. 1 seed Quinnipiac, a 84-75 winner over Monmouth, in the semifinals on March 7.
David Hicks chipped in 11 points and Kenny Onyechi and Jaytornah Wisseh added 10 each for Long Island.
Alvin Mofunanya had 11 points and 11 rebounds for the Knights.