Wright had 20 points and eight rebounds to lead NDSU (16-5, 5-1 Summit) and Braun added 11 points.
Lawrence Alexander was 3 of 3 from 3-point range and finished with 12 points for the Bison who shot 6 of 13 as a team from long distance. NDSU trailed 61-56 before going on a 10-2 run to close out the game.
South Dakota (8-12, 3-3) had been trailing for 25 minutes when Trey Norris' layup pulled the Coyotes even at 52. They took their first lead since the early minutes at 57-56 on Brandon Bos' jumper with 5:28 left which sparked a 6-0 run.
Authorities say former Michigan State basketball player Keith Appling has been charged with carrying a concealed weapon and other crimes after being found in possession of guns and marijuana.
Point guard Jaylen Fisher, who reopened his recruitment after coaching changes at UNLV, has committed to TCU over a long list of schools.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.