Miller finished 14th in the slalom after finishing second in Saturday's downhill race. Jean-Baptiste Grange of France won the slalom on Sunday.

Phil Mahre set the American record of 27 World Cup victories more than two decades ago.

"It's a nice record, something you dream about as a kid," the 30-year-old Miller said. "As a professional skier, you're more focussed on winning each individual race. Before the season, it was my target to break that record and it's a really good feeling if you reach your goals."

Benjamin Raich was second in the combined and went back to the top of the overall World Cup standings.

The 27-year-old Grange, who led after the first leg, finished in a two-run combined time of 1 minute, 45.04 seconds. The Frenchman edged Jens Byggmark by 0.15 seconds, and Mario Matt took third.

American Ted Ligety, who faced a 0.74-second deficit, started fast in his second run but lost control of a ski at the bumpy upper part of the course. He finished eighth.

"That's an OK result for me," Ligety said. "Grange is on fire these days. He is invincible."

Grange wasn't flawless in the first section of his second run and lost his 0.33-second advantage to Jens Byggmark. In the lower part, Grange accelerated for a strong finish.

"Everything's going very smooth for me these days," Grange said. "I am concentrating well and I know that I am a fast skier. Winning in Kitzbuehel is a big moment for me."

Grange won a slalom in Alta Badia, Italy, in December and a super-combi and a slalom race in Wengen, Switzerland, last week, and extended his lead in the slalom standings in front of Raich.

Byggmark, a two-time winner in Kitzbuehel last year, took risks in his final run.

"It did not work out completely well, but I am happy with this result," Byggmark said.

Julien Lizeroux was second going into the final run but dropped to fourth for his best career World Cup result.

Matt and some other skiers used specially prepared slalom skies with a hole in the front part for a better balance.

"I had two extreme errors, otherwise everything would have been possible today," Matt said.

Marc Gini, who won a slalom at Reiteralm, Austria, earlier this season, missed a gate in his first run and did not finish.