Gatens sealed the game with another 3-pointer that put Iowa ahead 63-48 after Zach McCabe dived to the court to corral a loose ball at midcourt and stop a potential Michigan fast break.
Freshman point guard Trey Burke led Michigan (14-4, 4-2) with 19 points despite sitting out much of the first half after picking up two fouls. Leading scorer Tim Hardaway Jr. added nine points but struggled throughout, shooting 2 of 13 from the field.
With the loss, the Wolverines fell out of a tie for second place in the Big Ten and failed to pick up their first conference road win.
Reserve forward Aaron White added 12 points and McCabe had 11 for Iowa, which outrebounded the Wolverines 39-30.
The Hawkeyes finished the half on an 11-5 run to take a 33-23 lead. The run included two big plays by Marble: an acrobatic left-handed layup as part of a three-point play, and a fadeaway jumper from the right wing that beat the buzzer and brought the crowd at Carver Hawkeye Arena to its feet.
Michigan struggled in the first half with poor shooting, including making just 3 of 16 3-point shots attempts, and had eight turnovers.
In the second half, the Wolverines cut Iowa's lead to 43-37 before Basabe's finger roll in the lane started Iowa's decisive 10-0 run.
For the game, Gatens was 4 of 7 from behind the arc and 5 of 5 from the free throw line. He had three steals and played good defense throughout on Hardaway.
The victory helps Iowa get past two ugly blowouts that dampened fan enthusiasm that had been high after the team achieved consecutive Big Ten road wins for the first time since 2007.
No. 5 Ohio State pummeled Iowa 76-47 in front of a near sellout crowd at Carver Hawkeye Arena a week ago. No. 6 Michigan State beat Iowa 95-61 in a game that saw Hawkeyes coach Fran McCaffery slam a folding chair to the court as he berated his players.