Routley finished the 103-mile stage from Monterey in three hours, 48 minutes and 37 seconds to take line honours ahead of second-placed American Gregory Daniel and Kevin De Mesmaeker of Belgium.
The 2012 Tour de France champion Wiggins completed the stage 77 seconds behind Routley, but increased his overall lead to 28 seconds over Australian Rohan Dennis.
Six riders jumped loose of the peloton early in the stage and Routley defended his climber's jersey by taking top points from the final two categorised climbs.
To the surprise of many, he also had enough left to unleash a race-winning sprint to the line, flying down the right side of the road to win a career-first stage in California.
The tour continues Thursday with a 107-mile stage from Pismo Beach to Santa Barbara.
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