With the Fighting Sioux (12-14) ahead 59-56, Anderson's baseline jumper with the shot clock expiring gave North Dakota a five-point cushion with 1:32 remaining. Anderson hit four free throws and Mitchell two in the final 40 seconds to seal it.
Mitchell had four 3-pointers and two blocked shots to become just the second player in North Dakota history to score 1,000 points, grab 500 rebounds and block 150 shots, joining Chris Gardner (1990-94).
The Lancers (9-17), who suited up only seven players, led by seven in the first half, but the Fighting Sioux got to 28-28 at halftime.
After North Dakota took a 50-38 lead, Longwood scored 10 straight, with Martiz Washington scoring the final eight, but the Fighting Sioux answered with a 9-0 run.
Antwan Carter's 21 points led the Lancers.
- Fighting Sioux
- North Dakota