Nearly halfway through his Stanford career, kicker Jet Toner has the best field-goal percentage in school history.

He missed just one attempt this year, his first, a 38-yarder against San Diego State that went wide left. Since then, he has made 14 in a row and 32 consecutive extra points.

For his career, he’s 35-for-41 on field-goal tries, an 85.4 percent clip. If the redshirt sophomore can keep up this pace, he would surpass his immediate predecessor, Conrad Ukropina , as the most accurate kicker in school history. Ukropina made 42 of 51 (82.4 percent) to lead all Cardinal kickers with at least 20 tries.

Toner also has extended his streak of extra-point tries without a miss to 86. And he has done all of this without being fully healthy most of the season, although neither he nor the coaches will discuss the injury.

“It happened early in the season, and I was able to play through it,” he said. “Then it got to the point where the head trainer and I said the wheels fell off.”

The 6-foot-4 Hawaiian missed the Washington game (in which his presence might have made a difference in a four-point loss) and the next game against Oregon State. He’s still not quite 100 percent, he said recently, but hopes to be by the time the Cardinal play Pittsburgh in the Sun Bowl in El Paso, Texas, on Monday.

Sun Bowl Who: Stanford (8-4) vs. Pittsburgh (7-6) When: 11 a.m. Monday Where: El Paso, Texas TV: Channel: 5Channel: 13Channel: 46 Radio: 680, 1050

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He made second-team All-Pac-12 after a season in which he had career-long 46-yard field goals against UC Davis and Notre Dame and provided 11 points in the 23-13 win at Cal. But his biggest moment was the tying 32-yarder as regulation time expired at Oregon; the Cardinal won in overtime 38-31.

A crowd of more than 58,000 at Autzen Stadium in Eugene was screaming, but Toner said, “In the moment, you’re not hearing anything. The offense did their thing and set me up pretty well.”

“Jet’s been awesome — very systematic in his approach, smooth, consistent,” head coach David Shaw said. “I’m excited where he is now, and I’m excited for his growth over the next couple of years. I think he’s going to be one of the best in America.”

And about that one miss ...

“I was a little excited — first game of the year,” he said. “After that kick, I settled down and focused on the next one, and kept moving through the season.”

With Jake Bailey graduating, Toner hopes to add kickoff duties next season, but he’ll have to beat out incoming freshman Ryan Sanborn, who booted 66 touchbacks out of 75 career kickoffs in high school in San Diego.

Freshmen to the rescue: Shaw said the team’s freshmen “helped save our season” after an unprecedented rash of injuries. Among the main contributors, wide receiver Michael Wilson and defensive end Thomas Booker played in every game. Cornerback Kendall Williamson took part in nine and defensive end Andres Fox six.

Several freshmen received action but can retain their redshirt status even if they play in the bowl game (the limit is four games). Wide receiver Simi Fehoko, cornerback Ethan Bonner and linebacker Ricky Miezan have played in three games. Linebackers Tangaloa Kaufusi and Jacob Mangum-Farrar, offensive tackle Grant Pease, fullback Jay Symonds, running back Justus Woods and quarterback Jack West have played in two.

Sophomore guard Foster Sarell and junior wide receiver Donald Stewart have played in three games, so they could play in El Paso and use this year as a redshirt season. On the other hand, wide receiver Connor Wedington has played in four, so he would lose his redshirt status if he plays.

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