Rhamel Brown added seven points and seven rebounds for the sixth-seeded Jaspers (14-17), who started the season 6-14 but have won eight of their last 11 including an upset of third-seeded Loyola 55-52 in the tournament quarterfinals.
Fairfield led 16-5 following a 6-0 run with 8:27 remaining in the first half. But Alvarado's three-point play on Manhattan's next possession sparked a 34-13 run that spanned both halves.
Brown capped the run with a layup as the Jaspers led 39-29 midway through the second period. The Stags never got any closer than five from there.
Manhattan shot 53.8 percent (7 of 13) in the second half, compared to 6-of-21 shooting for Fairfield (19-15), and committed just eight turnovers all game.
Maurice Borrow scored 15 for Fairfield.