Stanford’s slim playoff hopes depend on beating USC

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Coming off one of the best games of the year in college football, Stanford is bracing for another classic matchup. And Cardinal coach David Shaw expects it to be an “older-school” game against USC for the Pac-12 championship.

The conference’s two private schools both have physical ground games, veteran quarterbacks who operate efficiently and dynamic return people, he said Monday.

Saturday’s 4:45 p.m. game at Levi’s Stadium is a rematch of the Sept. 19 game in Los Angeles, in which Stanford upset the Trojans, ranked No. 6 at the time, by a score of 41-31.

“Defensively, we’ve got to eliminate the explosive plays,” Shaw said. The Trojans are probably “getting excited’’ watching tapes of recent Stanford games “because we’ve given up a lot of explosive plays,” he said.

Besides trying to reach the Rose Bowl for the third time in four years, the Cardinal (10-2, 8-1 Pac-12) have an outside shot of making the four-team field for the College Football Playoff. In addition to beating USC (8-4, 6-3) for the second time, they would need North Carolina to upset unbeaten Clemson in the ACC title game or Florida to shock Alabama in the SEC title game.

Stanford jumped from No. 13 to No. 7 in the AP poll this week and will rise from last week’s No. 9 spot in the new CFP rankings, coming out Tuesday, as a result of its dramatic 38-36 win over Notre Dame.

Shaw applauded USC’s selection of interim coach Clay Helton as its new head coach. Helton has guided the Trojans to a 5-2 record since taking over for the fired Steve Sarkisian.

“I think it’s well deserved,” Shaw said. “He’s very well respected in coaching circles. Stability is always good for the coaching profession.”

Southern California running back Justin Davis (22), left, runs for a short gain as Colorado linebacker Rick Gamboa (32) comes in for the tackle in the second half of an NCAA college football game Friday, Nov. 13, 2015, in Boulder, Colo. Southern California won 27-24. (AP Photo/David Zalubowski) less Southern California running back Justin Davis (22), left, runs for a short gain as Colorado linebacker Rick Gamboa (32) comes in for the tackle in the second half of an NCAA college football game Friday, Nov. ... more Photo: David Zalubowski, Associated Press Photo: David Zalubowski, Associated Press Image 1 of / 4 Caption Close Stanford’s slim playoff hopes depend on beating USC 1 / 4 Back to Gallery

Helton has moved the Trojans into more of a power running game since taking over. They have outrushed every opponent since then. They ran for 235 yards, including 103 in the fourth quarter, in their 40-21 trouncing of UCLA on Saturday.

It made “a lot of sense to recommit to the running game,” Shaw said, because the Trojans have a powerful offensive line and excellent tailbacks in Justin Davis and Ronald Jones II. Davis rushed for 130 yards against UCLA, and Jones supplanted Charles White as the top freshman rusher in USC history.

Davis “has size, quickness and vision,” Shaw said. “And the young cat is just explosive. It’s a great one-two punch.”

Stanford was limited to 153 yards rushing by Notre Dame but won behind Kevin Hogan’s four touchdown passes and Conrad Ukropina’s 45-yard field goal as time ran out.

Shaw hung onto his three timeouts even as the Irish were pushing to a go-ahead touchdown with just 30 seconds left. “I love having the timeouts for the offense as opposed to using them on the defense,” he said.

He and his staff talked about letting the Irish score, as former Notre Dame coach Charlie Weis did when the shoe was on the other foot in 2009. The Irish conceded a touchdown to Stanford with just over a minute left and hit a long pass play but failed on a Hail Mary pass and lost 45-38.

Shaw decided against a similar strategy even though it would have given his offense more time to move into field-goal range. “We had an opportunity to try to have a goal-line stand, and we wanted to give the defense a chance to win the game,” he said.

The Cardinal hope to have injured cornerbacks Ronnie Harris and Alijah Holder back for the USC game. Holder seems closer to playing than Harris, Shaw indicated.

Tom FitzGerald is a San Francisco Chronicle staff writer. E-mail: tfitzgerald@sfchronicle.com Twitter: @tomgfitzgerald

Pac-12 Championship

Who: Stanford (10-2, 8-1) vs. USC (8-4, 6-3)

Where: Levi’s Stadium

When: 4:45 p.m. Saturday

TV/Radio: ESPN/1050