The controversial three-time Tour de France winner attacked seven kilometres from the finish to come home clear of Venezuelan climber Jose Rujano at the 1892m summit on the south side of the Sicilian volcano.
Italian hope Stefano Garzelli won the battle for third, 50sec behind, with his compatriot Vincenzo Nibali in fourth.
Contador inherited the race leader's pink jersey from Rabobank's Dutch rider Pieter Weening, who had held the lead since last Wednesday's fifth stage.
He has a 59sec cushion over Belarusian Kanstantsin Siutsou, with France's Christophe Le Mevel third, at 1min 19sec.
Contador, who had started the stage in fifth after finishing second the day before, is aiming for a repeat Giro victory after winning on his only previous appearance in the race in 2008.
But this was the first time the 28-year-old had prevailed in an individual stage.
He said: "The wind was gusting up the ascent and I knew I had to attack between eight and five kilometres out.
"I wasn't thinking about the pink jersey. The race is only beginning, the Giro is hard and anything can happen."
Contador is competing here while still awaiting a ruling from the Court of Arbitration for Sport, which could overturn a Spanish cycling federation decision to clear him of any wrongdoing following a positive test for clenbuterol at last year's Tour de France.
And he reflected: "I dedicate this win above all to my fans, it's they who have given me the strength to keep going, and also to my family, who have been there for me through the tough times, to my team and my sponsors."
In Sunday's 169 kilometre run, a group of nine riders held sway for much of the day, this breakaway group holding a three-minute advantage going into the closing 20km.
Belgian's Jan Bakelants was out on his own 9km from the line, with Contador making his decisive to move two kilometres later.
Local rider Michele Scarponi tried his hardest to catch Contador but it was ultimately Rujano who got closest, crossing three seconds behind the pre-race favourite.
Monday is a rest day.
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