MarQueis Gray passed for 104 yards and rushed for 20 yards and a score for Minnesota (1-5, 0-2). The Gophers tried to bounce back from a 58-0 loss to Michigan but lost their third straight.
Purdue rushed for 217 yards on 47 carries.
Purdue had a false start on its first offensive play a week after committing 13 penalties in a 38-10 loss to Notre Dame, but the mistakes were few after that against the Gophers. Ralph Bolden's 2-yard run gave the Boilermakers a 7-0 lead.
Carson Wiggs hit a season-long 53-yard field goal to increase Purdue's lead to 10-0 with 5:18 left in the first quarter.
Minnesota's Donnell Kirkwood fumbled and Russell recovered at the Minnesota 11-yard line. The Boilermakers went for it on fourth-and-goal, and Shavers extended the ball to the pylon and scored to push the lead to 17-0.
Gray, who missed the Michigan game with a toe injury, replaced starter Max Shortell and got a rude welcome back. Allen jumped a route, intercepted a pass and returned it 37 yards for a touchdown to give the Boilermakers a 24-0 lead. It was the third touchdown return of Allen's career, tying Mike Rose and Rod Woodson for the most in school history. The 24 points were the most Purdue has scored in a quarter since producing 24 in the Indiana game in 2008.
Robert Marve entered the game at quarterback in the second quarter and threw a 12-yard touchdown pass to Ross that gave the Boilermakers a 31-0 lead with 4:08 left in the second quarter.
Minnesota finally got on the board with a 47-yard field goal by Chris Hawthorne, breaking a run of 95 consecutive points by its opponents. Purdue held Minnesota to 88 yards and six first downs in the first half to lead 31-3 at the break.
TerBush returned in the third quarter and led a 12-play, 86-yard scoring drive. His 24-yard touchdown pass on a screen to Shavers gave Purdue a 38-3 lead.
Raheem Mostert's 25-yard touchdown run gave Purdue a 45-3 lead late in the third quarter.
Minnesota's Marcus Jones returned the kickoff 92 yards for Minnesota's first touchdown since the fourth quarter against North Dakota State two weeks ago.
Gray's 1-yard touchdown run cut Purdue's lead to 45-17 midway through the fourth quarter.