Indiana State (5-1) got 14 points from Jordan Printy. Jake Odum had 13.
Following several late lead changes, Minnesota went up 69-66 on Armelin's layup and two free throws by Welch with 1:24 remaining.
After Steve McWhorter missed a 3 on Indiana State's next possession, Armelin made it 71-66 after hitting two more free throws.
Dwayne Lathan's three-point play gave Indiana State a 52-44 lead seven minutes into the second half. Trailing by nine, at 58-49, Minnesota rallied to go up 63-62 on Welch's basket with 3 1/2 minutes to play.
Indiana State, on the strength of 3s by Carl Richard, Odum and Printy, took an 11-5 lead early on.
A 3-pointer by Oto Osenieks and Welch's jumper put Minnesota up 15-13 seven minutes into the game. Hollins' long-range shot and a 15-footer by Mbakwe extended the Golden Gophers' advantage to 27-20 with 7 minutes left in the half.
Printy, who had 11 first-half points, hit a 3 during a 10-2 run as Indiana State grabbed a 30-29 lead with 4 minutes remaining in the half. The Sycamores led 40-33 at the half after R.J. Mahurin hit a 3 with 4 seconds to go.
Mbakwe and teammate Rodney Williams, who combined for 34 points in Minnesota's 86-55 win over DePaul on Thursday, had just two points overall during the opening half. Ralph Sampson III, playing with a bad ankle, didn't score in seven first-half minutes.
Williams and Sampson finished with three points and one point, respectively.