STANFORD, Calif. -- Conrad Ukropina, the hero of No. 9 Stanford's riveting 38-36 victory over No. 6 Notre Dame, insists he had a vision of how the final few seconds of Saturday's game would play out.

"With about a minute and half left, I was talking to our punter, and I said, 'Dude, I'm calling it right now. They're going to score, and we're going to get the ball back with 30 seconds left and win.'"

Indeed, the Irish did take a 36-35 lead on a 2-yard touchdown run by Notre Dame quarterback DeShone Kizer with 30 seconds left, finishing an impressive 88-yard drive that consumed 6:18.

But Stanford, with the benefit of a 15-yard facemask penalty with 20 seconds left and a 27-yard completion by quarterback Kevin Hogan to wide receiver Devon Cajuste with 10 seconds remaining, got in position for Ukropina to kick a game-winning 45-yard field goal on the game's final play.

It was the eighth lead change of the game, and the last-second defeat ended Notre Dame's hopes of landing a berth in the College Football Playoff.

"It's tough to talk to our team in the locker room after a game like that," coach Brian Kelly said. "We're two plays away from being undefeated and being No. 1 in the country."

The Irish (10-2) lost to Clemson by two points when Notre Dame's two-point conversion attempt failed with seven seconds remaining.

Meanwhile, the result meant euphoria for Hogan, who grew up as a Notre Dame fan and whose father attended Notre Dame.

"This meant the world to me," said Hogan, a fifth-year senior who completed 17 of 21 passes for 269 yards, four touchdowns, no interceptions and the last-minute game-winning drive in his final home game. "Going to Notre Dame games as a kid, being a fan. I couldn't have pictured it any better."

While Notre Dame's regular season is over, Stanford (10-2) still has a game remaining, as it will face Southern California in the Pac-12 championship game next Saturday in Santa Clara, Calif.

The Irish had two players rush for more than 100 yards. Kizer ran for 128, and running back Josh Adams, who started in place of injured C.J. Prosise, set a Notre Dame record for a freshman with 168 yards.

In addition, Notre Dame had three big plays that resulted in touchdowns: C.J. Sanders' 93-yard kickoff return, wide receiver Will Fuller's 73-yard reception and running back Josh Adams' 62-yard run.

The Irish had 533 yards of offense to Stanford's 422. But despite all this, the Irish still lost.

"I'm completely blank inside," Kizer said. "It's hard to describe how I feel. Tonight Stanford made one more play than us."

Kizer completed 13 of 25 passes for 234 yards, one touchdown and no interceptions, and wide receiver Will Fuller had six receptions for 136 yards and one touchdown

Cardinal running back Christian McCaffrey rushed for 94 yards. Cajuste caught five passes for 125 yards, including that key 27-yard catch with 10 seconds remaining.

Notre Dame took the lead for the first time 20-14 on Kizer's perfectly thrown 73-yard touchdown pass to Fuller with 2:15 left in the first half.

The Cardinal regained the lead 48 seconds before halftime on Hogan's 14-yard scoring pass to wide receiver Michael Rector, putting Stanford ahead 21-20..

Justin Yoon's 29-yard field goal early in the third quarter gave Notre Dame a 23-21 lead, but Stanford went back in front 28-23 on a 76-yard drive that ended with running back Remound Wright's 1-yard run.

Adams' 62-yard scoring run put the Irish ahead 29-28, when a two-point conversion attempt failed. But Stanford regained the lead 35-29 on tight end Austin Hooper's 10-yard touchdown reception on the first play of the fourth quarter.

Then came the critical scoring drives by each team, culminating with Ukopina trotting out for his first field-goal attempt of the game.

"To be honest," Ukropina said, "at that point I wasn't thinking about anything."

As his boot went through, Stanford kept alive its slim hopes of a berth on the College Football Playoff, while Notre Dame's chances ended.

NOTES: Notre Dame RB C.J. Prosise (ankle) and CB KeiVarae Russell (foot) did not play because of injuries suffered last week. Prosise is averaging 131.7 rushing yards per game this season, and Russell is considered the Irish's top cover man. ... Stanford starting CB Ronnie Harris (ankle) missed his second straight game. His replacement last week, CB Alijah Holder (undisclosed), did not play Saturday. Cardinal starting FB Daniel Marx (lower leg) did not play either.