Xavier became the eighth and last of the lower-seeded teams to win in the 16 tournament games played Friday. The Musketeers are seeded 10th in the region and will take part in a very unexpected matchup with Lehigh Sunday.
Lehigh became one of the two No. 15 seeds to win Friday when it knocked off Duke.
Notre Dame took a 63-60 lead with 1:03 to play on a 3-pointer from Jerian Grant but the Fighting Irish did not score again.
Lyons brought Xavier within one by making a layup with 42 seconds to go and the Musketeers took the lead on Tu Holloway's jumper with 24 seconds remaining.
Grant missed a 3-point attempt with 8 seconds left, leading to three Xavier free throws in four attempts down the stretch by Dezmine Wells.
The Big East Conference began the tournament with nine teams in the event and after every team has played at least once there are still six teams alive from the league. Notre Dame joined defending champion Connecticut and West Virginia on the sidelines from the Big East.
Holloway hit 10-of-15 shots from the field and scored 25 points to lead Xavier (21-12), which finished third in the Atlantic 10 Conference and lost to St. Bonaventure in the finals of the league tourney.
Jack Cooley had 18 points for Notre Dame (22-11).