Isaiah Lamb added 14 points. Parker's double-double was the first for Marist (3-6) this season.
Army, which had made at least 10 3-pointers in nine straight games, sank only 7 of 38 Sunday, missing their first 15.
Tanner Plomb scored 27 points for the Black Knights (8-3), but was just 3 of 11 from the arc. Dylan Cox added 16 points and Kevin Ferguson 13 plus 13 rebounds for his seventh career double-double. Kyle Wilson, who was fifth in the nation in 3-pointers per game, made just 2 of 13 and scored eight points.
Marist built an eight-point lead with 1:19 left. Army got within four with 33 seconds remaining but three free throws from Parker and two from Hart ensured the win.