Reichelt avoided the mistakes of his rivals and was cheered by 50,000 spectators when the green light for the fastest time appeared in the finish area at an event watched by Arnold Schwarzenegger and Formula One boss Bernie Ecclestone.
Reichelt mastered the Streif course in 2 minutes, 3.38 seconds. Overall World Cup leader Aksel Lund Svindal trailed by 0.21 in second, and Miller was 0.34 behind in third.
"This is like dream," said Reichelt, and admitted he had "little tears in my eyes" during the flower ceremony.
Miller dominated the only training session on Thursday, but had a costly mistake when he came off the race line at the Seidalm section halfway down the course on Saturday. He finished in the top three in a downhill for the first time in nearly two years after missing last year because of knee surgery.
"Winning training runs doesn't do it for you," Miller said. "You've got to execute on race day. It's too many times that I've made these stupid mistakes that aren't really forced. They are not forced errors. It's not on a tough part of the course, it's just a real basic part. So, it's pretty heartbreaking.
"I knew it when I came across the finish line, that I'd just wasted another opportunity to win this course."
Miller said he picked the race as the right time to peak before the Olympics. The American worked closely on his setup with technician Chris Krause, who was Didier Cuche's serviceman when the Swiss standout won three years in a row from 2010-12.
"I've been skiing well and I had good confidence and knew what I had to do," Miller said. "It's just execution, and in downhill skiing execution is what matters.
Michael Walchhofer was the last Austrian to win in Kitzbuehel in 2006, and Reichelt's victory will be a big boost to the Austrian men's team two weeks before the start of the Sochi Olympics. The former "Wunderteam" left Vancouver without a single medal four years ago.
"Being an Austrian, coming down this course and winning here in front of all these fans, is a huge present," he said. "This is a real highlight of my career. If you win here, you are a legend."
Until 15 minutes before the race, Reichelt wasn't even sure he was going to start. Suffering from persistent back problem, the 33-year-old Austrian did some free skiing to find out whether he would be able to compete without pain.
"I wasn't feeling too well yesterday," Reichelt said.
Reichelt celebrated his seventh career win but only second in the discipline. Reichelt was also the last Austrian to win a World Cup downhill in 2012 in Bormio, Italy.
By finishing runner-up, Svindal extended his lead in the overall standings to 102 points over second-place Marcel Hirscher of Austria, who doesn't compete in downhill.
Svindal also tops the downhill standings, leading Reichelt by 440-360 points.
The Norwegian, who won a super-G here last year, is still chasing his first downhill win at the Streif.
"Coming second in Kitzbuehel isn't too bad for a result," Svindal said. "Bode had a mistake, otherwise he would have been unbeatable. I was happy that I was ahead of him when I finished, but I knew you could be faster. And Hannes showed just that."
The weekend ends with two World Cup events Sunday, a super-G race that counts as the first portion of a super-combined, followed by one floodlit slalom run.