Salnave, who coughed up the ball against the Iona full-court pressure that quickly turned into Rickey McGill's tying 3-pointer with 13.3 seconds remaining, waited as time wound down before driving into the lane and floating a shot over a defender and off the glass.
McGill had made three free throws with 22.5 seconds left that cut the deficit to 81-78. It was the second time in the final minute McGill earned and made three free throws. Meanwhile, the Hawks went 1 for 2 at the line twice in a three-second span as Salnave drew an offensive foul on McGill on an inbounds play.
Salnave had 19 points and Deion Hammond 15 for the Hawks (6-14, 5-2 Metro Atlantic Athletic Conference), who have won four straight.
Asante Gist led the Gaels (6-11, 4-2) with 21 points, McGill had 18 and Tajuan Agee 20 with 10 rebounds.
Neither team led by more than eight and the game was tied 16 times. In the second half, there were 36 fouls, four technicals and a combined 42-of-57 performance from the foul line. The biggest difference was Monmouth had a 20-2 advantage in second-chance points.