Kent State led by as many as 19 points in the second half, but Bowling Green would not go away easily without an attempted rally. The Falcons cut the lead to 76-70 on a layup by Torian Oglesby with 2:20 left in the game.
But Greene scored on a layup then he and Porrini each made two free throws to give the Golden Flashes enough cushion with an 11-point lead.
Scott Thomas scored 23 points for the Falcons (7-9, 1-2). Jordan Crawford had a double-double with 10 points and 13 rebounds.