SOUTH BEND, Ind. -- During Notre Dame's team walk-through before Saturday's game against No. 1 Clemson, coach Brian Kelly issued a proclamation, and a warning.

"I just want you to know," Kelly told the players, "When we win this thing, the fans are going to storm the field."

Kelly added that because of the COVID-19 pandemic, which includes a recent rise in cases on Notre Dame's campus, the players needed to exit the field as soon as possible after the game.

"Coach Kelly, you might as well call him a prophet," linebacker Jeremiah Owusu-Koramoah said. "Prophet Kelly."

Kelly's words came true moments after No. 4 Notre Dame completed a 47-40 win over Clemson in two overtimes Saturday night at Notre Dame Stadium. Students stormed the field from all four corners of the stands, creating a mass celebration in the middle of the field. Notre Dame limits attendance to students, faculty and university personnel -- other than players' families -- and while Saturday's game drew only 11,011, most of them seemed to enter the field at the end.

"With COVID being as it is, we've got to get off the field and get to the tunnel," Kelly said. "Now I beat 'em all to the tunnel. So that didn't go over so good, but they reminded me that I did tell them that, so my skills of prognostication were pretty good today."

Notre Dame's public-address announcer repeatedly asked fans to leave the field, but many remained for several minutes.

Clemson players and coaches quickly exited to the tunnel in the northeast corner of the field, while most Notre Dame players and coaches headed for their tunnel. Clemson coach Dabo Swinney said he didn't mind the field rush from the Notre Dame fans, saying, "It was an epic game."

Notre Dame running back Kyren Williams said he was late getting to the postgame locker room celebration because he had to get through so many fans who had entered the field.

"That was a cool experience for me, everybody rushing down," said Williams, who had never witnessed a field storm before Saturday. "Coach Kelly told us before the game that it was going to happen. ... He told us to get inside after the game, fast."

Wide receiver Avery Davis said he got "bumped around" during the field storm but added, "I loved the energy."

The ACC did not immediately respond to a request for comment about the field storm at Notre Dame, a league member in football this season. Notre Dame recorded its ninth win against an AP No. 1 team and ended Clemson's 36-game regular-season win streak Saturday.

"It's something you expect with our great fans and our great community around us, they're really, really passionate about us playing football," Owusu-Koramoah said. "You expect something like that, storming the field, beating the No. 1 team. [Kelly] told us to get up out of there if they did storm the field, but it's kind of hard, so we just celebrated with them."

Senior quarterback Ian Book rallied Notre Dame to a late touchdown to force overtime, and then led two touchdown drives in the extra sessions.

"A night I'll never forget, no matter how old I am, I know I'll remember this game forever," Book said. "Just a special moment. ... When the fans stormed the field, it was actually pretty cool. It was really fun."

The university on Tuesday reported 38 positive tests, followed by 71 positive tests on Wednesday and 29 on Thursday. Notre Dame's football team went through an outbreak in late September that forced a Sept. 24 game at Wake Forest to be postponed until Dec. 12.

Notre Dame president the Rev. John Jenkins tested positive for COVID-19 in early October, and has received increased scrutiny for his approach toward the virus after he appeared at the White House Rose Garden Ceremony to celebrate the nomination of Supreme Court Justice Amy Coney Barrett.