Hincapie's Discovery Channel teammate Lance Armstrong retained the yellow jersey he is aiming to win for a seventh consecutive time before retiring after the race on July 24.
The race will resume with a third and final day in the mountains following Monday's rest day.
On what was the second of three days in the Pyrenees, and with six major climbs the toughest stage on the race, Armstrong's challengers were never going to launch an audacious attack too early.
It was no surprise that when a group of 14 riders formed after an early attack by Dutchman Michael Boogerd they were allowed to build a solid lead, which hit a maximum of 18 minutes.
But as they stage leaders slogged their way over the first of the day's climbs, the searing temperatures and continuous effort began to take their toll. One by one the 14-man group began to thin out until only six riders rode over the summit of the Peyresourde -- the fourth Col of the day -- with a 12-minute lead on Armstrong's group, which in turn was also beginning to break up.
Behind them Ivan Basso's Spanish teammate Carlos Sastre, Australian Cadel Evans and France's Christophe Moreau were dropped and they were soon joined by Liberty duo, Jorg Jaksche and Alberto Contador. Jaksche and Evans managed to rejoin the chasing peloton a kilometer before the summit. It was a wise decision given the two difficult climbs still remaining.
The leaders had lost four minutes to the peloton on the Peyresourde climb, and on the subsequent 7.5km climb to Louron-Azet the pace of Armstrong's team thinned out their group.
The first significant attack came from Basso, who pulled away from Armstrong, who soon followed the Italian. Both briefly distanced Jan Ullrich but the German managed to grapple his way back. His T-Mobile teammate Alexandre Vinokourov was left trailing and ended up in the small group which was being led by the race's best climber, Michael Rasmussen, in a bid to keep in touch with the trio.
Armstrong, Basso and Ullrich came over the Louron-Azet summit with a 7:40 deficit on the six leaders, who had already began the tricky 18km descent towards the day's final climb in earnest.
At the front meanwhile Oscar Sevilla's attack on the first kilometers of the final climb was countered by Oscar Pereiro. The former was left trailing as his Spanish compatriot raced with Hincapie and Boogerd towards the summit finish.
Hincapie looked the freshest, given his lack of relaying the lead group for most of the day -- and again the New Yorker was happy to sit on Pereiro's wheel for the 10.7km final ascent.
Given their lead, the stage victory appeared all but settled. It only remained to be seen who out of Armstrong's group was hit the hardest.<!--pagebreak-->
Basso attacked shortly after starting the climb, and seconds later was followed by Armstrong -- and this time their lead on Ullrich looked more promising. Basso and Armstrong's pace left the German around 15 seconds in arrears and holding on. The scene being played out a few minutes ahead of them saw Italian Pietro Caucchioli rejoin the three leaders who had dropped him at the foot of the last climb.<!--noad-->
Caucchioli then stunned the leaders by attacking with four kilometers to race. Pereiro, then Hincapie followed and soon left the Italian behind.
Pereiro was trying to shake the American off his wheel, but there was further drama when the cameraman who was filming them on a motorbike crashed into one of two spectators who were running rather too close to the two riders.
However in the final meters Pereiro had no answer to Hincapie, who took a well-deserved victory.Joel Saget/AFP/Getty Images A motorcyclist hits a fan as George Hincapie (left) and Oscar Pereiro battle to the finish
Top 10 results, Stage 15: Lezat-sur-Leze - Saint-Lary Soulan (Pla d'Adet) (205.5 km)
George Hincapie (USA/DIS) 6:06:38
2. Oscar Pereiro (ESP/PHO) at 0:06
3. Pietro Caucchioli (ITA/C.A) 0:38
4. Michael Boogerd (NED/RAB) 0:57
5. Laurent Brochard (FRA/BOU) 2:19
6. Ivan Basso (ITA/CSC) 5:04
7. Lance Armstrong (USA/DIS) 5:04
8. Oscar Sevilla (ESP/MOB) 6:28
9. Jan Ullrich (GER/MOB) 6:28
10. Michael Rasmussen (DEN/RAB) 6:32
Stage 15: Complete results
Top 10, Overall standings
1. Lance Armstrong (USA/DIS) 62:09:59
2. Ivan Basso (ITA/CSC) @ 2:46
3. Michael Rasmussen (DEN/RAB) 3:09
4. Jan Ullrich (GER/MOB) 5:58
5. Francisco Mancebo (ESP/BAL) 6:31
6. Levi Leipheimer (USA/GRL) 7:35
7. Floyd Landis (USA/PHO) 9:33
8. Alexander Vinokourov (KAZ/MOB) 9:38
9. Christophe Moreau (FRA/C.A) 11:47
10. Andreas Kloden (GER/MOB) 12:01
Stage 15: Complete overall standings
Stage 15: Category standings