Iowa will take on Maryland next Tuesday in New York with both teams having advanced to the tournament's semifinals by eliminating a No. 1 seed.
Maryland ousted Alabama, the Crimson Tide having been the top seed in that quarter of the bracket.
Virginia held a 41-39 lead with 13:30 to play when Iowa embarked on a 19-5 surge that decided the game.
The 3-pointer Marble hit to start the outburst was the only one he made in five attempts, but he led the Hawkeyes (24-12) with 24 points and five assists. Adam Woodbury and Zach McCabe added 10 points each for Iowa, which finished alone in sixth place in the Big Ten Conference this season with a breakeven record in the league.
Virginia (23-12) was paced by 24 points from Justin Anderson, who made 5-of-8 from 3-point range.