Blake Hoffarber added 13 points, five rebounds and four assists, helping the Gophers withstand another strong shooting night from an opponent.
Ralph Sampson III scored 13 points for Minnesota (7-1), which recovered from Monday's loss to Virginia in the Big Ten/ACC Challenge, the first home non-conference loss since Tubby Smith became coach in 2007.
"We needed to get this win, no matter which way," Smith said. "I thought our guys really showed a lot of grit, something they didn't do against Virginia. We were behind and we were tested. You could feel the pressure on our guys to make plays, and they did."
Errick Peck scored 16 points for Cornell (2-6). Chris Wroblewski added 16 points for the Big Red, who lost their fifth straight game. Cornell made 14 of 33 3-pointers.
"It's something that is the strength of our team, and we haven't shot the ball well," Big Red coach Bill Courtney said. "We'll continue to take good ones and I think we did a good job of getting and taking open looks tonight."
The Big Red hit five of their first 10 from outside the 3-point arc, allowing them to stay with the taller Gophers.
"We emphasized it in practice this week, but they were just getting open somehow," Hoffarber said. "We've got to take a look at that on film, but just get your hand out and get right in their face."
Minnesota was 5 of 16 from downtown, but the Gophers' size advantage eventually helped them pull away in the second half, mostly by allowing Minnesota to get to the free-throw line.
"It's something we're going to get better at," Smith said of the free-throw shooting. "I wish we had played like this against Virginia. Going inside more and we probably would have won that game. That tells me we're at least getting the ball inside and those free throws will start falling for us."
The Gophers shot 26 of 44 from the free-throw line, while Cornell finished 10 of 14.
That kept Minnesota in the game even though the Gophers went without a field goal for an 11-minute stretch in the second half.
Mbakwe went 12 of 20 from the free-throw line, helping to overcome 0 for 4 shooting.