Iowa looked sure to win when Yared Hagos scored at 17:48 of the third period. But Jay Harrison brought the Marlies to within one just under a minute later, and Tyson Nash sent it to overtime with just 11 seconds left to play.
Kevin Baker scored Toronto's other two goals.
Junior Lessard, with two, and Janos Vas scored for Iowa.
Jean-Francois Racine made 13 saves for Toronto (16-21-2-3), while Dan Ellis stopped 35 shots for Iowa (21-17-1-1).