The former Tour de France winner and four-time Olympic champion set the pace on the Mount Diablo climb, even as his supporting team-mates started to drop, before fading to finish ninth, 20 seconds behind stage winner Rohan Dennis.
His overall lead heading into the fourth stage is now 24 seconds while fellow British rider Adam Yates, a winner of the recent Tour of Turkey, showed his climbing skills to finish fourth, rising to fifth in the general classification.
And Wiggins paid tribute to his Team Sky team-mates for their support.
“The boys did a good job in this heat," he said.
"I was alone about the last eight kilometers I think. We did this climb a little over a week ago. I knew how it kicked up the last 300 metres.
"It was a tough climb. Every day is a tough day when you’re in yellow."
Wednesday's fourth stage sees the riders take on the flatter ocean roads between Monterey to Cambria.
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