The 13th-ranked Michigan Wolverines also advanced, fighting off Minnesota in overtime 73-69. No. 12 Wisconsin eliminated No. 15 Indiana in the quarterfinals with a 79-71 win and No. 7 Ohio State ran away from Purdue 88-71.
Michigan State (25-7) shot 70 percent from the field in the first half and put together a game-breaking, 19-4 run that gave the Spartans a 15-point halftime lead. Green scored 21 points and Michigan State hit 32-of-55 shots for the game.
Adreian Payne chipped in 16 for Michigan State while Keith Appling added 12 and Brandon Wood 10. Those three were a combined 14-of-18 shooting.
Iowa (17-16) got 20 points from Josh Oglesby with Zach McCabe (13), and Roy Devyn Marble (12) and Mat Gatens (10) also reaching double figures.
Rob Wilson popped in 30 points for Wisconsin (24-8), which will meet Michigan State in the semifinals.
Wilson, who entered the game averaging 3.1 points a game, connected on 11-of-16 shots from the floor and hit 7-of-10 from 3-point range.
Wilson and Jared Berggren, who finished with 16 points, scored 11 consecutive points for Wisconsin to give the Badgers a 72-65 lead with 38 seconds to go.
Indiana (25-8) got 17 points each from Jordan Hulls, Christian Watford and Cody Zeller.
Michigan escaped against Northwestern when Evan Smotrycz made a 3-pointer with 18 seconds left in regulation to forge a 56-56 tie. The Wolverines (24-8) then got four free throws from Trey Burke and Tim Hardaway Jr. during the final 22 seconds to hold on for the win.
Burke scored 30 points and Hardaway had 20.
Andre Hollins led Minnesota (19-14) with 21 points.
Ohio State set up a semifinal meeting with Michigan, with Jared Sullinger scoring 30 points and pulling down 11 rebounds. Purdue (21-12) was within six points with 6:45 to go but the Buckeyes (26-6) closed the game on a 23-10 run.
Purdue got 20 points from D.J. Byrd.
Michigan State defeated Wisconsin in both their regular-season meetings this season. Michigan and Ohio State split their two games.