For 20 minutes, Purdue went punch for punch with Houston, taking a two point lead in front of an Indianapolis, Indiana crowd just an hour from Purdue's campus in West Lafayette.
But Houston got one offensive rebound too many, and a late game charge fell just short as Houston's Milos Uzan ends Purdue's season in the Sweet Sixteen with a last second lay up, giving the Cougars the 62-60 win.
After falling behind 56-46 in the second half, Matt Painter's Boilers found a final charge.
Myles Colvin hit a mid range and Fletcher Loyer knocked down a floater for a 4-0 run, and a Camden Heide three cut the game to 57-53 with just over five minutes to play.