Walker finished with seven points on 1-of-5 shooting, but went 5-of-6 from the line.
Andre Hollins led Minnesota (16-9, 5-7 Big Ten) with 20 points, making 7-of-14 from the field.
"We beat a very good team, a very well-coached team," Minnesota coach Richard Pitino said. "I've got a lot of respect for them. I thought our guys stepped up when they needed to."
Iowa (15-9, 6-5) came within two points with 20 seconds left after Jarrod Uthoff sank two free throws. But Minnesota's Nate Mason made 1-of-2 from the line with 19 seconds left and Walker sealed it.
Uthoff finished with 17 points and seven boards for Iowa.
"We just weren't very good from the start," said Aaron White, who finished with 13 points for Iowa. "We weren't shooting open shots. We weren't moving well."
Minnesota, winners of three straight, snapped the Hawkeyes' two-game winning streak. The Gophers shot just 40 percent from the field, making just 23-of-57 shots, including 6-of-19 from behind the arc.
In the first 10 minutes, Iowa made six of its first 13 shots. Minnesota sank 5-of-15 and missed all five of its 3-point shots. Iowa led 15-11 after an Adam Woodbury mid-range jumper with 9:21 left. It would be the last bucket for the Hawkeyes for eight-plus minutes.
Minnesota, meanwhile, scored nine straight for a 20-15 lead, and entered halftime up 23-19.
"It's frustrating, but that's going to happen," Iowa's Mike Gesell said of the scoring drought. "Especially playing in the Big Ten, it's going to happen. Minnesota is a very good defensive team, and when that does happen, we have to rely on getting shots and we weren't able to do that."
The Hawkeyes regained the lead, a 31-30 advantage, with 13:30 to play in the second half. Then, with a little over eight minutes to play, White's alley-oop dunk brought Iowa back within two, as Minnesota led 41-39.
The Gophers scored nine of the next 12 points for a 50-42 lead, and held a 57-50 lead with less than two minutes to play. Iowa closed to within three points with 55 seconds left, then came within two after Uthoff's free throws.
Gesell, who missed all four of his shots, turned the ball over with 11 seconds left, then fouled immediately after, and Walker went to the line to clinch the win.
"He got it essentially to the front of the rim," Iowa coach Fran McCaffery said. "The kid, Walker, made a nice play. He poked it from him."