Rob Poole scored 19 points, hitting 5 of 7 3-pointers for the ninth-seeded Saints (8-23), who play top seed Niagara Saturday.
After Jay Bowie's 3-pointer tied it for the 12th time at 64-64 with 1:43 left, the eighth-seeded Red Foxes couldn't score again. Marist missed seven shots, five from long range, ending its three-game winning streak.
Trenity Burdine's free throw broke the tie with 1:01 left. He then scored on a layup. Anosike made a foul shot with 20 seconds remaining and, after four missed shots by Marist, dunked with 3 seconds showing.
Chavaughn Lewis' 24 points paced the Red Foxes (10-21), who led 56-52 with 5:53 left.
Siena, which led 32-31 at halftime, is 6-0 all-time against Marist in MAAC tourney play.
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