The Spaniard won last year's Tour de France by 39 seconds from Luxembourg's Andy Schleck.
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But the Dane was outgunned and Rebellin burst past Schleck and Australia's Cadel Evans to secure his triumph.
Schleck ensured he will wear the yellow jersey for a second day as the top 10 of the general classification standings remained unchanged.
The 2010 champion Andy Schleck missed this year's race with a broken pelvis, while Spain's Alberto Contador is still serving a ban for doping offenses.
The big loser overall was Luxembourg's Frank Schleck, who was caught by his CSC teammate Sastre for three minutes, and slipped from second to sixth overall.
But Frank Schleck of Luxembourg, who finished third overall last year, lost nearly half a minute to Wiggins, coming home 135th at 38 seconds behind teammate Cancellara.
Top contenders now include 35-year-old Russian Denis Menchov, a two-time Tour of Spain winner, the Schleck brothers and the 2008 Tour de France winner Carlos Sastre of Spain.
So, with the dramatic backdrop of the Champs Elysees beckoning, Sastre has the yellow jersey, Oscar Freire the green, Bernard Kohl the polka dots, and Andy Schleck the white.
Contador, given a retrospective two-year ban which ends after this year's Tour de France, is set to make his return at the Tour of Spain where Andy Schleck hopes to compete.
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The 2012 Tour was thought to be well-suited to Wiggins' strength as a time-trial rider, and the absence of contenders like Alberto Contador (banned) and Andy Schleck (injured) opened up the field.
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It completes a miserable 2012 for Schleck, who has been forced to abandon preparatory stage races such as Paris-Nice, the Tour of Catalunya and the Dauphine through a mixture of injury and illness.
CNN: 2010 champion Andy Schleck out of this year's Tour de France
Saxo Bank, including Luxembourg's Andy and Frank Schleck and Swiss time trial world champion Fabian Cancellara, were third, 12 seconds behind the winners and two seconds off the Liquigas outfit of Italy's Vincenzo Nibali.
On Col d' Agnes, 45km from the finish, Luxembourg's Andy Schleck also tried to spring free but the Astana team, a permanent fixture at the front of the pack, reacted instantly and ensured their two big stars stayed out of danger.
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