Greene's first of two made free throws with 9:44 remaining was number 1,000 and his second capped a 17-4 run which erased a 52-40 deficit and gave UMBC (8-11, 2-5 America East) a 57-56 lead with 9:44 remaining.
UMBC's best chance occurred when Albany committed a shot clock violation with 1:11 remaining and leading 75-70. Junior forward Justin Fry (New Bloomfield, Pa.) was set up for a 3-point attempt at the top of the key with 1:01 to play, but his shot was too strong and Albany grabbed the rebound and hit two additional free throws to seal the win.
Albany came into the game hitting 28.5 percent from behind the arc and hitting only 4.3 treys per game, but made 10 of 18 in the contest. UA sophomore guard Tim Ambrose led all scorers with 26 points.