Schleck overtook Frenchman Thomas Voeckler on the final day of racing in the Alps, making up a 15-second deficit during a steep 68-mile stage.
"My motivation is super, my legs are good, my condition is there," Schleck said. "So I'm confident I can keep this till Paris."
Voeckler cracked on the first of three daunting climbs. He never caught the leaders despite a gritty struggle and gave up the yellow jersey after wearing it for 10 days.
With the race ending Sunday in Paris, Schleck leads brother Frank by 53 seconds. Australia's Cadel Evans is third, 57 seconds behind.
Frenchman Pierre Rolland captured the 19th stage, rewarding thousands of wildly cheering French fans who packed the finish. He attacked near the end of the mountain's 21 punishing bends, dropping three-time champion Alberto Contador and Olympic champ Samuel Sanchez.
"I grew up watching Lance Armstrong and Marco Pantani, watching how they climb the Alpe d'Huez," Rolland said. "Now I've won the Alpe d'Huez. It's going to take a minute to sink in."
Andy Schleck is considered one of the best climbers. But Evans still has every chance of beating both brothers in today's 26-mile time trial in Grenoble, the next-to-last stage.
The time trial, an individual race-against-the-clock race, has long been Schleck's weak point. Evans is strong in this discipline, but it will take a superlative performance to make up 57 seconds and spoil the Schlecks' dream of becoming the first brothers to finish on the winner's podium together in the Tour.
"Everybody tells me it's a time trial that suits me good, so I believe everybody and hope to show a good performance tomorrow," Andy Schleck said.
In 2008, Evans beat Andy Schleck by nearly two minutes in a time trial that was about six miles longer. Andy Schleck was only 23 and riding in his first Tour.
Evans will follow a simple strategy today: "Start as fast as possible, finish as fast as possible, hope you're fast enough."
Andy Schleck, who lost the 2010 Tour by just 39 seconds to Contador, made good on Thursday's promise to claim the yellow jersey.
On Friday, Andy Schleck rode much of the time in a small group alongside Contador. But he chose not to follow the Spaniard when he attacked at the bottom of the 8.5-mile Alpe d'Huez.
"I had no interest in chasing Contador or Sanchez," Andy Schleck said, with neither rider in contention for the yellow jersey. "Today I had bigger goals than to win the stage."
Rolland, who rides for Europcar and is in his third Tour, attacked as the stage drew to a tense finish toward the top of the 6,100-foot final climb. He clenched his fists and grinned widely as he crossed the line 14 seconds ahead of Sanchez and 23 ahead of Contador.
Andy Schleck rode in 57 seconds behind Rolland in a group of six riders that included his brother and Evans. Voeckler arrived 3 minutes, 21 seconds behind Rolland. He dropped to fourth place overall, 2:10 behind.