Alejandro Valverde, of the Baleares team, won the 10th stage held over 178.5km between Grenoble after beating Armstrong in a two-man race for the finish line -- and the American was sporting enough to shake the young Spaniard's hand immediately afterwards.
Overnight race leader Jens Voigt, of the CSC team, finished well off the pace on a first day in the Alps which featured two category one climbs and the first summit finish of the race.
Germany's 1997 winner Jan Ullrich came over the finish line among a group of riders at around 2 minutes, 20 seconds behind Armstrong and is now over four minutes behind his American rival.
Italian Ivan Basso, of the CSC team, came in at just over a minute behind while Ullrich's T-Mobile teammate Alexandre Vinokourov also fell away on the 21km climb to the alpine ski station, the Kazakh finishing almost five minutes behind.
Armstrong, who began the day in third place overall at 2:18 behind Voigt, now has firm control of the race ahead of Wednesday's second day in the Alps where the first unclassified climbs of the race await his challengers.
He leads Rasmussen by 38 seconds, Basso by 2:20 and Frenchman Christophe Moreau by 2:42.
After benefiting from the work of his Discovery Channel team for most of the day, the 33-year-old American came into his own in the final 15km of the 21km-climb to the summit finish of Courchevel.
By the time they had completed a few kilometers of the day's second climb, Armstrong decided it was time to take over the operation. His furious pace up the category one climb had devastating effects. Despite their efforts, it left Ullrich, Vinokourov and Basso all struggling and one by one they fell out of contention.
Armstrong ended up leading a group of five riders on the final 10km of the climb, whose average gradient was six percent.
Dane Michael Rasmussen, wearing the polka dot jersey for the race's best climber so far, did well to hang on while Valverde hung on beside his teammate Francisco Mancebo.
With less than five kilometers to race, Ullrich was already 1:28 behind Armstrong -- meaning the German's hopes of upstaging the American on his retirement race were slowly slipping away.
Armstrong meanwhile upped the pace further for his companions with just four kilometers to go, and again shortly after Rasmussen had tried to break away a kilometer further on.Franck Fife/AFP/Getty Images Alejandro Valverde comes in just ahead of Armstrong in a two-man race for the finish line
In what was a thrilling finale, Armstrong broke away from the group shortly after they had passed through the tunnel beside the kilometer to go mark, but he was pursued by Valverde.
Armstrong's efforts to get to the finish line appeared to damage his chances of the stage win in the end -- Valverde was hanging on his back wheel, and easily overtook the American in the final 50 meters to claim his first ever stage victory on the race.
Top 10 results, Stage 10: Grenoble - Courchevel (178.5 km)
1. Alejandro Valverde (SPA/BAL) 4:50:35
2. Lance Armstrong (USA/DIS) at 0:00
3. Michael Rasmussen (DEN/RAB) 0:09
4. Francisco Mancebo (SPA/BAL) 0:09
5. Ivan Basso (ITA/CSC) 1:02
6. Levi Leipheimer (USA/GRL) 1:15
7. Eddy Mazzoleni (ITA/LAM) 2:14
8. Cadel Evans (AUS/DAV) 2:14
9. Andreas Kloden (GER/MOB) 2:14
10. Andrei Kashechkin (KAZ/C.A) 2:14
Stage 10: Complete results
Top 10, Overall standings
1. Lance Armstrong (USA/DIS) 37:11:04
2. Michael Rasmussen (DEN/RAB) @ 0:38
3. Ivan Basso (ITA/CSC) 2:40
4. Christophe Moreau (FRA/C.A) 2:42
5. Alejandro Valverde (SPA/BAL) 3:16
6. Levi Leipheimer (USA/GRL) 3:58
7. Francisco Mancebo (SPA/BAL) 4:00
8. Jan Ullrich (GER/MOB) 4:02
9. Andreas Kloden (GER/MOB) 4:16
10. Floyd Landis (USA/PHO) 4:16
Stage 10: Complete overall standings
Stage 10: Category standings