Riding without his teammates, who couldn't keep up on the day's last two climbs, Armstrong held off his main rivals to place second ahead of Italy's Ivan Basso, with Jan Ullrich of Germany fourth.
The six-time champion's overall lead over Mickael Rasmussen of Denmark grew to one minute, 41 seconds. Rasmussen, who had been just 38 seconds behind at the start of the day, placed eighth on the stage up to the ski station of Ax-3 Domaines.
The brutal 220.5-kilometer (137-mile) trek was raced under scorching sun. A sheen of sweat glistened on Armstrong's arms. Riders poured water over themselves to try to cool down.
Armstrong's teammates deserted him when Ullrich's rival T-Mobile squad piled on speed going into the day's hardest ascent, a 15.1-kilometer (9.4-mile) climb over the Port de Pailheres. It peaks at 2,001 meters (6,565 feet) and is so hard that it is classified as "hors categorie" -- or unrated.
"T-Mobile was basically sprinting," said Armstrong. "The downside was that I was left alone."
But he soaked up the pressure.
"You either fight back or you run away," he said.
He stayed with Ullrich, Basso and others, and then dished out some punishment of his own on the final climb up to Ax-3 Domaines, powering up the ascent. Neither Basso nor Ullrich could get past him -- and in the end, he left both behind.
"It was a very tactical day, with the attack from the T-Mobile," said Armstrong. "The heat, the distance, it was hard, it was a very hard day."
Armstrong's lead over Basso grew to 2:46. Basso managed to stay with the American up to Ax-3 Domaines but couldn't follow his sprint for the line.
Ullrich fell away toward the top of the ascent, when Armstrong accelerated. His overall deficit to Armstrong grew to 4:34.
Totschnig, 34, was part of a group of riders that escaped from the main pack shortly after the start in the Mediterranean town of Agde. He managed to shake off the other members of the group on the Port de Pailheres ascent, and then clung on from there up the final climb to win.
He finished 56 seconds ahead of Armstrong for his first stage win in the Tour and broke into tears. The Austrian's time was five hours, 43 minutes and 43 seconds. He jumped eight spots in the overall standings to 14th, still 10:39 behind Armstrong.
"An extraordinary day," Totschnig said. "I didn't think it was possible to win a stage like that."
Armstrong's highest-placed teammate was Yaroslav Popovych, 16th in the stage, 4:18 off Totschnig's time. Usually, Armstrong looks to his support riders to lead him up the Tour's climbs. But they have not been quite as dominant this year. Armstrong also found himself alone with T-Mobile rivals on a climb in week two of the three-week race.
T-Mobile racer Alexandre Vinokourov had said before Saturday's stage that their aim was "to make Lance's team explode."
"We'll attack from the first bump," he said. But at the end of the day, he had to concede defeat. Vinokourov, third in 2003, was 11th on Saturday, falling back to 7:09 behind Armstrong overall.
"Lance was strong," he said.
On Sunday comes what Armstrong called "the hardest day of the Tour" -- a relentless 205.5-kilometer (127.7-mile) route from Lezat-sur-Leze that has a succession of five climbs before an "hors categorie" uphill finish to Saint-Lary Soulan.
Armstrong said that final ascent is critical, especially after an exhausting day on Saturday.
Monday is a rest day before the last high mountain stage. Then come three less-demanding portions before a time trial on the Tour's penultimate day. Armstrong hopes to win that stage and then ride into Paris to collect a seventh consecutive title on July 24 -- when he will retire.Joel Saget/AFP/Getty Images On his own, Lance Armstrong joins the leading group with (from left) Jan Ullrich, Kazakh Andrey Kashechkin and Alexandre Vinokourov
Top 10 results, Stage 14: Agde - Ax-Trois Domaines (220.5 km)
1. Georg Totschnig (AUT/GRL) 5:43:43
2. Lance Armstrong (USA/DIS) at 0:56
3. Ivan Basso (ITA/CSC) 0:58
4. Jan Ullrich (GER/MOB) 1:16
5. Levi Leipheimer (USA/GRL) 1:31
6. Floyd Landis (USA/PHO) 1:31
7. Francisco Mancebo (ESP/BAL) 1:47
8. Michael Rasmussen (DEN/RAB) 1:47
9. Andreas Kloden (GER/MOB) 2:06
10. Haimar Zubeldia (ESP/EUS) 2:20
Stage 14: Complete results
Top 10, Overall standings
1. Lance Armstrong (USA/DIS) 55:58:17
2. Michael Rasmussen (DEN/RAB) at 1:41
3. Ivan Basso (ITA/CSC) 2:46
4. Jan Ullrich (GER/MOB) 4:34
5. Levi Leipheimer (USA/GRL) 4:45
6. Floyd Landis (USA/PHO) 5:03
7. Francisco Mancebo (ESP/BAL) 5:03
8. Andreas Kloden (GER/MOB) 5:38
9. Alexander Vinokourov (KAZ/MOB) 7:09
10. Christophe Moreau (FRA/C.A) 8:37
Stage 14: Complete overall standings
Stage 14: Category standings