Once Marble and White got it going, the 14th-ranked Hawkeyes overwhelmed Minnesota.
White scored all of his 18 points in the second half and Oglesby came off the bench to add a season-high 17 points as Iowa blew past Minnesota 94-73 on Sunday.
Oglesby led yet another brilliant effort by Iowa's reserves, who scored 43 points.
"It's just a further example of the talent we have across the board," Iowa coach Fran McCaffery said. "When you're having 40 points off the bench, it presents all kinds of problems for them."
Iowa (15-3, 4-1 Big Ten) overcame a 10-point deficit with a 29-10 run and finished the game by outscoring the Gophers 61-30.
Andre Hollins had a game-high 20 points for Minnesota (14-5, 3-3). But Iowa held Hollins without a field goal in the second half in handing the Gophers their most lopsided loss of the season.
"They just decided to shut him down, obviously," Minnesota coach Richard Pitino said of Hollins. "Our offense wasn't the issue. It was absolutely our defense."
Last season, Iowa used a 37-10 run to erase a 16-point deficit and beat the Gophers handily in Iowa City.
On Sunday, the Hawkeyes outscored the Gophers by 19 points in just 6 1/2 minutes to notch their 20th straight home win -- one shy of the Carver-Hawkeye Arena record.
An 11-0 run helped put Minnesota ahead 43-33 late in the first half, but Oglesby hit back-to-back 3s as the Hawkeyes got the deficit down to 2 by halftime.
Marble then got rolling, scoring 14 points in the opening 8:41 of the second half to help Iowa take a 71-59 lead with 11:19 left.
"I trust his decision making and his commitment to winning. When he gets going like that, it just has such an incredible effect, not only on our team but everybody that was here. The reaction of the crowd was really special," McCaffery said.
White's 3-point play with 4:35 left was a back-breaker for the Gophers, who missed all eight of their 3-point tries in the second half.
"They've got the ability to make a deep run at this. I was really impressed with them," Pitino said. "We were certainly humbled, and maybe we needed it."
Austin Hollins had 13 for the Gophers, who came to Iowa City on a roll.
After pushing league leaders Michigan State to overtime in East Lansing, Minnesota beat No. 11 Ohio State 63-53 on Thursday for its third win in four games.
The Gophers started strong in this one too, keeping Marble and White scoreless for nearly 18 minutes in the first half. But Oglesby capped a brilliant half with an off-balance 25-footer that pulled the Hawkeyes within 43-41.
Oglesby, who missed the first 12 games with a foot injury, had 14 first-half points to keep the Hawkeyes in the game.
"He brings such dynamic perimeter shooting. It's something we need," Marble said of Oglesby. "When he's shooting well, it really opens up the rest of the offense."
Iowa had a week off after a program-defining upset at Ohio State, and then looked so sluggish in the first 20 minutes Sunday.
But Marble opened the second half with his first basket of the day and followed with a pair of 3s, waking up a sellout crowd and putting the Hawkeyes ahead 52-46.
Iowa is now a game back of Michigan for second place in the league -- but it won't have to wait long for a shot at the Wolverines.
Michigan hosts the Hawkeyes on Wednesday."It's tough. You win one on the road -- a big one on the road -- and you've got to wait a week to play. And then you see... Minnesota gets a big win and everyone is talking about them, how well they're playing. Obviously we have a confidence about ourselves and we realize that we can do something special with this group," White said.