Overnight Tour leader Schleck had just started to attack defending champion Contador on the gruelling Port de Bales climb, 25 kms from the finish line in Bagneres de Luchon, when he was stopped short as his chain came off.
Contador, who was 31 seconds behind Schleck at the start of the ride in Pamiers, capitalised on the Luxembourg rider's misfortune and surged ahead in the race for the final victory.
The stage victory was claimed by France's Thomas Voeckler, who had been part of an early breakaway.
Joining forces with third-placed Samuel Sanchez and fourth-placed Denis Menchov of Russia, Contador reached the summit of the Port de Bales with a 27-second lead over Schleck, whose yellow jersey was then hanging by a thread.
The Saxo Bank team leader, who has a poor record while riding downhill, lost more time in the descent to cross the line 39 seconds behind the 2007 and 2009 Tour winner.
Contador now leads Schleck by eight seconds in the overall standings with two more gruelling stages in the Pyrenees to go.
Sanchez lies third, two minutes behind, with Menchov fourth.
"The race is not finished and I will take my revenge in the next few days," Schleck said.
Contador was criticised by some people for his decision to capitalise on his rival's misfortune and Schleck added: "These guys don't get the first prize for fair play today."
The Spaniard, who was booed on the podium, said he was unaware that his rival had suffered technical problems.
"When I launched my attack, I was not aware of the incident. When I was told about it, we had a solid lead and we were going full gas," he said.
Contador was among the riders who waited for Schleck when he crashed in the second stage to Spa.
The day's honours went to French champion Voeckler, who was the first rider to win a Tour stage with the tricolour jersey in 16 years.
"To win a stage with the blue, white and red jersey is just extraordinary," Voeckler said.
With five stage victories, French riders have achieved their best collective performance in the Tour since 1997.
The battle between Contador and Schleck will resume on Tuesday with arguably the hardest stage in the Pyrenees over 199.5-kms to Pau with four classic passes, Peyresourde, Aspin, Tourmalet and Aubisque.