Rodney Williams added 16 for the Gophers.
American was led by Stephen Lumpkins with nine points. John Schoof had eight for the Eagles.
All five Minnesota starters — Williams and center Elliott Eliason with guards Austin Hollins, Andre Hollins and Joe Coleman — are back for Minnesota, which advanced to the NIT title game last season and is projected to be a middle-of-the-pack Big Ten team.
They were clearly a mismatch for the Eagles, who were picked to finish third in the Patriot League preseason poll behind Lehigh and Bucknell.
Minnesota was the aggressor from The Opening tip while American struggled on both ends of the floor.
Austin Hollins scored eight points during a 15-0 Gophers run to start the game, including a steal and dunk and a fast-break layup. Struggling against the Minnesota full-court press, American committed three turnovers, was 0 for 4 from the field and had no rebounds in the game's first 5 minutes.
Hollins, a junior, had two more steals and dunks during a 15-2 Minnesota run that put the game at 34-8 with 5:39 to play in the first half. American had 14 first-half turnovers that led to 17 Minnesota points.
Eliason and Coleman each had four points during a 10-0 run to make it 44-14 at the half.
A layup by Austin Hollins gave Minnesota a 60-26 lead midway through the second half.
American went more than 12 minutes without a basket in the second half — but made nine free throws — before Jesse Reed banked in a 3-pointer to make it 62-30.
Minnesota shot 43.5 percent for the game; American 23.7 percent.
Coach Tubby Smith quickly showcased the depth on this year's roster by getting 11 players into the game before it was 9 minutes old. That included Trevor Mbakwe and Mo Walker, both of whom are returning from knee injuries.
The 6-foot-8, 245-pound Mbakwe is in his sixth season of college basketball — his fourth at Minnesota after the NCAA granted him an extra season of eligibility. Through seven games last season, he showed he is one of the conference's best players by being the team's leading scorer (14.0) and rebounder (9.1) before tearing his right ACL. As a freshman at Marquette in 2007-08, he missed the majority of the year with a knee injury.
Mbakwe, who earlier this week tweeted that he would repay his athletic scholarship this year if the Gophers fail to make the NCAA tournament, looked shaky at times, especially on defense, but finished with four points, three rebounds and two blocks.
Mbakwe's absence was shorter than that of Walker, who also came off the bench to play in his first regular season game in almost two years. The redshirt sophomore tore the PCL and meniscus in his right knee on Dec. 23, 2010, then missed all of last season while dealing with complications from the injury. Walker had four points and two rebounds.