After Nicky Wieben put back an Amanda Nisleit miss, ISU forced a turnover and Heather Ezell banked in a deep 3-pointer to cut the lead to 68-66 with 50 seconds left.
The Cyclones' pressure forced another turnover and after a timeout, Alison Lacey drained her third 3-pointer of the game to give ISU its first lead since the 12:35 mark of the second half.
The Spartans had three chances in the final 25 second but each shot bounced off the rim, securing the win for the Cyclones.
Lacey finished with a game-high 29 points while Nisleit added 17 points and seven rebounds. Ezell was the only other ISU player to score more than three points, finishing with 14.
The Cyclones started ice cold to open the game, hitting just two of their first 15 field goal attempts to fall behind 13-4. Two Ezell 3-pointers sandwiched a MSU bucket to cut the lead to five at 15-10.
The Cyclones continued to trim the lead down and took their first lead with 6:02 remaining in the half on a long ball from Nisleit. The Spartans scored the next two buckets but ISU responded with a 7-2 run, which saw Lacey score all seven points, to go up 31-29. The Cyclones pushed the lead to four points twice and went into the break with a two-point lead despite shooting just 35.5 percent (11-31). Michigan State scorched the nets in the half, shooting 51.9 percent (14-27) from the floor.
ISU, which hit five 3-pointers in the opening stanza, had Nisleit (12 points), Lacey (12) and Ezell (10) account for 34 of its 38 points in the opening stanza. Allyssa DeHaan led the Spartans with 16 first-half points.
The Cyclones increased their lead to five points (49-44) with 14:50 left in the game before Michigan State went on a 9-3 run to take the lead. The Spartans held the advantage for the nearly 11 minutes before the Cyclones started the late rally.
The Spartans were led by DeHaan's career-high 24 points. Mia Johnson finished with 13 points in her final game.
Iowa State will face the winner of the Stanford/Ohio State game Monday at 8 p.m. (CT) on ESPN with the winner advancing to the Final Four in St. Louis, Mo.