Hall, who tied NMU's Ricky Volcy with a game-high 28 points, fell one three-point basket shy of tying the school-record for treys in a game as he connected on 7-of-9 from behind the arc.
The game, which saw 14 lead changes and seven ties, was played back and forth for much of the contest.
South Dakota started the game with a David Nour (Armour) steal at 19:40, which turned into the first of Hall's three-pointers 10 seconds later. The USD lead eventually diminished, but was later returned to a three-point Coyote advantage, 14-11, when redshirt freshman Jesse Becker (Plymouth, MN) connected on a three at 12:58, assisted by freshman Mitch Begeman (Sioux Falls).
Northern Michigan proceeded to go on an 11-0 run to lead 22-14 at the 10:11 mark, that was stopped by Nour with a three of his own at 9:32. However, NMU would lead the remainder of the half and post a 38-35 margin at the break.
In the second half, USD picked up the defense and with Volcy on the bench with four fouls, re-took the lead at 9:29 on a pair of Hall free throws.
Until the 3:36 mark, when the Coyotes took the lead for good on a jumper in the paint by senior All-American Turner Trofholz (Schuyler, NE), no team had a lead greater than two points.
After the bucket by Trofholz, USD knocked down seven of its 10 free throws to seal the win.
While each team had three players score in double figures, USD collected 17 from outside sources, while the Wildcats had just two other players score six points each.
Trofholz finished in double figures for the 36th consecutive time by posting 15 points and pulling down eight rebounds, while Nour tallied 12 points and led all players with six assists.
NMU garnered 16 points from Randy Alexandre, who was a perfect 6-of-6 from the field and made 4-of-5 free throws, and 12 points from Nick Buck. Volcy led all players with 11 rebounds to complete the double-double.
For the game, USD shot 42.9 percent (21-of-49), including 12-of-28 (42.9 percent) from downtown. The Coyotes earned 26 foul shots in the game, 10 more than their opponent, and connected on 18 for 69.2 percent.
USD, who was outrebounded by Northern Michigan, 39-34, forced 19 Wildcat turnovers that led to 20 points.
NMU shot 44.8 percent (26-of-58) from the field, made 8-of-27 three's (29.6 percent) and converted just 8-of-16 attempts (50 percent).