Luke Donald, meanwhile, found himself in a familiar position, in second place.
In 11 starts at Harbour Town, Donald has finished in the top three six times.
He headed for the clubhouse one off joint leaders Graham DeLaet and Luke Donald, but Cauley's flawless 63 nudged him ahead of the pack and into the outright lead.
American Bud Cauley leads on eight under, dropping no shots in his round. The conditions couldn't have been better for the first round, as they seemed to suit Donald's game just fine.
But a return to Hilton Head Island allowed him to rekindle his form of old in the opening round, which included five birdies and an eagle on the par-5 second hole.
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Hamilton and Vettel are now tied at the top spot on driver standings with 43 points each as both of them have won a race each. Second-place finisher Sebastian Vettel, for his part, had high praise for the performance of his Mercedes competitor.
"It's never fun to be sitting at home", Donald said. Obviously I've had a lot of success here in the last eight years - I've done everything but win.
The 27-year-old birdied four of his final five holes - including his last three - to grab the lead in SC. "It would be nice to give myself another chance to finally get over that hurdle".
After missing the cut at his past two Tour starts, including the Masters, Rod Pampling, made a flying start with birdies at the first two holes before finishing with a two-under par 69 to be in a tie for 35th.
Defending champion Branden Grace and US Ryder Cup captain Jim Furyk were also nicely placed on three under, but Danny Willett (71), Graeme McDowell (72) and Matt Fitzpatrick (73) are likely to need something in the 60s on Friday to avoid an unscheduled weekend off.
Russell Henley continued his recent run of top-flight golf with a 66 to join a group that included former US Open victor Webb Simpson and Ian Poulter.
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