"I just kind of blanked (out) there. Some of the coaches were telling me. That was my fault," Pangos said. "I should have known the foul situation. If I knew I wouldn't have gone for it, but I just blanked."
Jordan Sibert scored 23 points in Dayton's third win against a top 12 team in seven games at the early-season tournament.
Dyshawn Pierre hit four free throws with less than 30 seconds left and Kyle Dranginis narrowly missed an open 3-pointer that could have tied it for the Bulldogs in the final seconds. Gonzaga (4-1) led by as many as 16 in the first half.
"We were battling foul trouble all game long so we had some strange lineups and scenarios out there, but Dayton did a great job staying with the game and they handed it to us," Gonzaga coach Mark Few said.
Sibert had 16 points in the second half as the Flyers (5-0) came back to give this year's tournament its first major upset.
"The second half, the guys were ready to play," Dayton coach Archie Miller said. "From that point forward, we were the team we wanted to be."
Sam Dower Jr. who sat on the bench with foul trouble during some critical possessions late in the game scored 18 points and shot 8 for 10 from the floor for the Bulldogs. Gary Bell Jr. had 12 points.
"We knew we were going to be in a dogfight after watching tape on these guys," Few said.
Dayton took its first lead during a 7-0 run with less than 12 minutes to play after cutting into Gonzaga's lead as soon as the second half began. From there, it was a back-and-forth game.
"Our guys weren't panicked at halftime at all," Miller said. "At halftime we talked about a few things and our guys were able to do those. The way we rebounded the ball and made shots, that's what college basketball is about."
Dayton shot nearly 61 percent in the second half after hitting less than one-third of its shots in the first 20 minutes. The Flyers responded each time Gonzaga attempted to regain control, hitting big shots and free throws to stave off any sustained comeback.
Pierre had 15 points and nine rebounds. Devin Oliver scored 12 and Khari Price 11 for the Flyers.
Dayton also beat No. 12 UConn and No. 6 Maryland during the 2000 tournament in Maui. The Flyers will play No. 18 Baylor on Tuesday with a spot in the finals at stake.
Gonzaga will play Division II Chaminade in the losers' bracket.
Oskar Garcia can be reached on Twitter at http://twitter.com/oskargarcia