Wiggins came home in the front group at the end of the 121.7km eighth stage to finish the race 30 seconds ahead of Rohan Dennis (Garmin-Sharp) and claim his first win of the season.
He then paid tribute to the team-mates who supported him over the three ascents of the Rock Store climb.
Wiggins said on the Team Sky website: “I say it every day, but without those guys I wouldn’t be in this position.
“You can’t do it on your own and, as strong as my performance was individually in the time trial, my team have taken the strain all week.
“Those young Americans in my team, Joe (Dombrowski), Ian (Boswell) and Danny (Pate) have done a fantastic job. Even (yesterday) they didn’t give up the chase and came back after they’d been distanced on the climbs. This is a fantastic way to finish.”
Seven riders managed to edge clear of the pack after a frantic opening, with Niki Terpstra (Omega Pharma-QuickStep) and Jack Bobridge (Belkin) breaking away from that group on the second climb.
But the pair were hauled in on the next ascent and the Team Sky riders were able to respond to further attacks to keep Wiggins well-placed.
Cavendish lost contact with the group late in the race, but his Omega Pharma team-mates worked hard to bring him back with around 10km to go and then give him the platform to launch his sprint finish.
The Manxman stayed on the wheel of Peter Sagan (Cannondale) before bursting through to take his second stage win of the race.