Three years ago, Fowler made three birdies in his final four holes to outlast fellow American Matt Kuchar in a dramatic finish at the course just down the road from Muirfield in eastern Scotland.
The tournament was played at different courses in 2016 and '17 but has returned to Gullane - and Fowler has picked up where he left off.
He made three straight birdies from No. 2, before driving the green at No. 6 and holing the eagle putt to reach the turn in 30.
After picking up more birdies on Nos. 11 and 12, the course record of 63 looked in danger but Fowler dropped a shot at the next hole after hitting into a bunker and parred his way in.
Fowler shared the lead with Robert Rock, Jens Dantorp and Scott Fernandez.
"The front was playing easier than the back," Fowler said, "and getting off and getting under par makes it a lot easier to hold on or try to get a couple extra on the way in.
Fowler's victory in 2015 prompted Gullane's members to rename the clubhouse bar in his honor.
"I feel like this golf course, you go around and you hit pretty much every club in your bag," he said. "You hit driver quite a bit. It's just fun. Especially once the wind starts to blow a bit."
Phil Mickelson started with an even-par 70.
The British Open takes place further up the east coast of Scotland at Carnoustie next week.
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