Meanwhile, it's back to the drawing board for BYU coach Dave Rose.
"There are a lot of things we need to do," he said, adding that "we need help at three positions."
Certainly, BYU needs better play from the point. Matt Carlino was 1 of 14 for the tournament.
"Ty played really well. Brandon played well when he was in, I thought," Carlino said. "But as a team, I don't think we played very well, myself especially. We just have to get better."
Mostly, Rose must find a way to overcome the loss of two post players Chris Collinsworth and Stephen Rogers, both of whom suffered career-ending injuries prior to the start of the season.
With Davies on the bench for 22 minutes, the Cougars (2-2) were outmanned inside and didn't do enough on the perimeter to make up the difference. Even Tyler Haws' scoring 21 points 44 for the Classic wasn't enough.
"It's definitely tough," said Haws about Davies' foul trouble. "He's a huge part of our team. He makes everyone better. He's going to play smarter in the next few games."
Notre Dame forward Jack Cooley had the size and strength to take on BYU's slender Ian Harward, in for Davies. Cooley finished with 19 points and 13 rebounds.
Jerian Grant also scored 19 points and Eric Atkins added 16 for Notre Dame.
"When you coach for 80 minutes in two games, coaching around foul situations ... that makes it difficult," Rose said. "We have to be smarter."
BYU had an opportunity to widen its 49-42 lead, but failed to take care of the ball. And in a game that featured 12 ties and 10 lead changes, those wasted chances hurt.
Then again, credit Notre Dame (3-1) for fighting its way back, especially on the heels of an overtime loss to Saint Joseph's the night before.
"We invested a lot of energy last night and had our hearts broken," Brey said. "I was impressed with our maturity. We may have gotten a bit better and found out about ourselves."
Notre Dame willed itself back into the game, going on a 16-2 run. The game was tied at 49-49 when Davies picked up his fourth foul midway through the second half.
When the Cougar forward returned with nearly six minutes to play, the Irish owned a 61-57 lead.
BYU pulled to within two points twice before Notre Dame made a final push.
Atkins buried a 3-pointer, BYU turned the ball over and Grant scored to give the Irish a 68-61 lead and control the rest of the way.
Storylines Irish 78, Cougars 68
R With BYU leading by seven early in the second half, Notre Dame goes on a 16-2 run.
• Tyler Haws leads BYU with 21 points.