The victory came in the championship game of the Diamond Head Classic and kept Iowa State unbeaten.
Iowa State began its parade to the foul line owning a two-point lead and Melvin Ejim hit two free throws with 19 seconds left. Derrick Marks made 1-of-2 and Ejim also converted 1-of-2 before Hogue hit the last two with six seconds to play.
The Cyclones improved to 11-0 and has a game remaining on New Year's Eve against Northern Illinois before heading into Big 12 Conference action. Iowa State is one of nine unbeaten teams left in major college basketball.
St. Mary's also came into this tournament with a perfect record, but lost all three games it played in Hawaii.
Iowa State rallied from a seven-point halftime deficit behind 23 points from DeAndre Kane and 16 from Georges Niang. The Cyclones made 11 more free throws than did Boise State to help offset 37 percent shooting from the field.
The Broncos (10-3) were led by Derrick Marks with 23 points.