The former Tour de France winner and four-time Olympic gold medallist covered the 20.3km route in 23 minutes 18 seconds, 44 seconds quicker than nearest rival, Australia's Rohan Dennis.
It means he took control of the general classification from fellow British rider Mark Cavendish, who had sprinted to victory on stage one.
“You have a plan in your head as to how you imagine you’re going to come out at the end of today, and so far it’s probably a bit better than I imagined,” said Wiggins.
“I think it’s going to be a tough week now. I think in stage three the race can really start. As big as the gaps may be now, everyone is in with a chance.”
Tuesday's 174.5km third stage sees riders tackle a course that will take them from San Jose to a summit finish at Mount Diablo.
- Sports & Recreation
- Tour de France
- Rohan Dennis
- Mark Cavendish