"I'm a complete rider, but I'm not good at the sprint - so I have to attack from far away. I am super happy."
Contador and his Astana team-mate Armstrong finished in the same group as Wiggins and Andy Schleck, 59 seconds back.
The stage was made up of two big climbs, including the highest point of this year's Tour at the top of the Col du Grand St Bernard, and ended with a long descent from the smaller Col du Petit St Bernard.
Schleck, who lies fifth overall, chose the second ascent to attack Contador but, despite the help of his brother Frank, the Luxembourger could not shake the 2007 champion or Wiggins, who doggedly stayed on his wheel throughout.
It was a difficult stage. When the Schlecks attacked, I was able to follow but it was not easy, especially to follow Andy, who is very strong
Armstrong did lose touch when Schleck went off the front of the peloton, however, and was 35 seconds adrift of the yellow jersey group at one stage but the seven-time champion kept his nerve and impressively clawed back the lost ground.
Carlos Sastre, last year's Tour winner, was also dropped but, although he took longer than the Texan to recover, fought his way back to the bunch containing the other contenders for this year's crown before the summit.
The race downhill to the finish was less eventful but still proved perilous as Schleck's Saxo Bank team-mate, German ride Jens Voigt, came off his bike when he hit a bump at high speed and was immediately taken to hospital.
"It was a difficult stage," Contador said. "When the Schlecks attacked, I was able to follow but it was not easy, especially to follow Andy, who is very strong.
"I'm not going to say I'm tired otherwise I'll be attacked on Wednesday but I am."
Contador also paid tribute to Armstrong, who vowed to help him win the Tour after being dropped on the climb up Verbier at the end of Sunday's stage.
"What Lance did proves once again what a great champion he is," added Contador.
"I'm sure he will be great help in the days to come."
Contador remains in control of the race but must negotiate another daunting day in the Alps on Wednesday that is sure to see more attacks from his rivals.
The 169.5km trek from Bourg St Maurice to Le Grand Bornand features five tough climbs and another downhill finish.
There are 161 riders left in this year's race after Voigt became the latest rider to withdraw.
The German temporarily lost consciousness after his fall and his Saxo Bank team manager Bjarne Riis said: "I only saw him after the crash and he looked very, very bad.
"It's not nice to lose a rider like this, but these are things which happen in a race and you have to accept them.
"It is too early to say how bad his injuries are, I didn't see the crash, I only saw the aftermath and it wasn't good.
"I am just concerned with Jens' health right now."
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