Minnesota (10-1) made 24-of-52 (.462) field goals and held a 38-26 advantage in rebounding, while forcing 18 St. Peter's turnovers.
The win was the eighth home victory without a defeat for the Gophers this season. Minnesota is in the midst of a six-game home stand, and stretched its winning streak to three games.
Unlike Tuesday's game versus Appalachian State, in which the Gophers fell behind 5-0 at the start, this afternoon Minnesota jumped ahead 6-0 behind a pair of three-pointers by Welch.
Darius Conley made a pair of 18-foot jumpers from essentially the same spot on the court on back-to-back possessions to cut it to 6-4, but Sampson found Welch along the baseline for a layup to give him the first eight points for the Gophers.
Sampson followed with the next six points for Minnesota, as the Gophers maintained their lead at 14-9, and freshman guard Joe Coleman made it 17-11 by nailing a three-pointer from in front of the St. Peter's bench.
A dunk by freshman forward Oto Osenieks gave Minnesota a 19-11 advantage, but the Peacocks answered with a 5-0 run, highlighted by a long-range trey by Chris Prescott to pull back within three points.
Minnesota responded with a 6-0 run of its own, with sophomore guard Austin Hollins tallying four points off Peacocks' turnovers, to extend its lead back to nine points, 25-16.
Conley did his best to keep St. Peter's close, as he scored four quick points to increase his total to 13 of the Peacocks' first 20 points and pull the visitors back within seven points.
But the Gophers closed the half by outscoring St. Peter's 7-3 over the final 4:11 to go to the locker room with their largest lead of the half, 34-23. Welch had 10 points in the half to lead the Gophers, while Conley led all scorers with 13 points.
Williams, who was held to four points in the first half, quickly equaled that total in the first couple minutes of the second half, and the Gophers opened a 14-point advantage at 41-27.
Sampson scored a layup on an assist from Williams to make it 43-27, but the Peacocks then cut into the lead by outscoring Minnesota 9-5 over the next three minutes.
Down the stretch, though, the Gophers were able to extend their lead and finished with the largest lead of the afternoon at 22 points.
Conley led St. Peter's with a career-high 20 points, while also adding a team-high seven rebounds. Prescott finished with 12 points, but the Peacocks were held to just 19-of-48 (.396) field goals, including 3-of-11 (.273) three-pointers.