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The 37-year-old Armstrong, who is competing in North America for the first time since his return from retirement, finished the 173.2-kilometer stage from Davis to Santa Rosa in a chasing group about two minutes off the pace.
His time-trial bike, valued at more than 10,000 U.S. dollars, was taken from a team truck in Sacramento where Armstrong had used it in Saturday's prologue. Road bikes belonging to three of his Astana teammates were also stolen.
Despite the loss, Armstrong said he thought he would be able to catch up with the leaders later in the nine-day tour.
"It was a tough day and we had to chase earlier than we planned but I'm confident I can take time back in the time trial," said the seven-time Tour de France winner, who trails Spain's Mancebo by one minute and five seconds.
With his win, Mancebo, of Rock Racing, moved from 40th position into a 1:02 lead over defending champion and Armstrong's teammate Levi Leipheimer with American compatriot David Zabriskie of Garmin-Slipstream third overall, trailing by 1:03.
Mancebo went to the front early and rode alone for much of the day before finishing in a time of 4:11.07.
Quickstep's Jurgen Van de Walle of Belgium was second, with Italian Vincenzo Nibali of Liquigas third.
Another Astana rider, Fabian Cancellara of Switzerland, who held a two-second race lead after capturing the prologue on Saturday, withdrew because of a virus.