The performance marked Anosike’s 13th double-double this season.
Evan Hymes added 21 points, Trenity Burdine came off the bench for 13, Rakeem Brookins added 12 and Rob Poole 11 for Siena (5-16, 3-7), which snapped a two-game losing streak.
Siena, whose point total was a season-high, shot a sizzling 63.6 percent (14 of 22) from the field and 11 of 12 from the free-throw line en route to a 41-33 lead at the break.
Marist (5-16, 2-8) trimmed the deficit to 78-75 with 40 seconds left but missed its final five shots, including three 3-pointers in the final 15 seconds.
Chavaughn Lewis led Marist with 23 points but the Red Foxes made just 7 of 23 shots from deep.