Matt Kavanagh, who scored four second-half goals, tied the game at 7 with 10:10 left and then put the Irish (11-4) ahead for good with less than six minutes remaining.
The Titans (5-10) were able to keep Notre Dame in check during the first half as Detroit took a 5-1 lead into halftime.
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Brandon Beauregard led the Titans with three goals.
The Irish will play next weekend against Duke or Loyola, which play today at 5:15p.m.
Yale 10, No. 8 Penn State 7: After trailing by four at halftime, the visiting Bulldogs (12-4) exploded out of the break and outscored the Nittany Lions 9-2 in the second half to advance to the second round.
Penn State (12-5) won all seven faceoffs in the first half and scored five unanswered goals to take a 5-1 halftime lead, but Yale started to click offensively in the second half and tied the game at 6 with 12:59 left.
The Bulldogs went on a 7-0 run through the final two quarters and led by as many as four in the fourth. Penn State turned the ball over nine times in the last period.
Colin Flaherty led the Bulldogs with three goals, and Eric Natale had 10 saves as Yale earned its first NCAA tournament victory since 1992.
The Bulldogs will play top-seeded Syracuse or Bryant in the quarterfinals next weekend in College Park.
After trailing by one in the first quarter, Denver finished the first half on a 6-2 run to take a 9-6 lead into halftime.
With one second left in the third quarter, Eric Law caught a long pass from Taylor Long and scored to give Denver a five-goal lead into the fourth. Law, a transfer from Salisbury, finished with four goals.
Denver will play next Sunday against North Carolina.
Lehigh led 2-1 after the first quarter but allowed five unanswered goals to start the second and couldn't overcome the deficit as North Carolina cruised in the second half.
Jimmy Bitter and Chad Tutton led the Tar Heels with three goals and one assist each. Holman's five points improved his career school record to 213.
The Patriot League champion Mountain Hawks were outshot 53-30 for the game as North Carolina extended the nation's longest current winning streak to 10.
Salisbury opened the game with four unanswered goals to assume control, but Washington & Lee cut the lead to three at halftime.