The Evans resident, who started his round on the 10th hole, holed out a 103-yard shot on his final hole, the par-4 ninth, for eagle.
It gave him 4-under-par 67 and share of the lead with Chad Campbell and Colt Knost.
Taylor, who got into the tournament on a sponsor exemption overcame a double bogey on his seventh hole but striking for three birdies and the eagle on his second nine, shooting 4-under 32.
“I hit a smooth one,” Taylor said of his eagle on his 18th hole. “Came off right, right at it, and fortunate enough to go in.”
Jim Furyk, the 2010 winner, was a stroke back along with former Georgia golfer Harris English, Charlie Wi and Matt Every.
Forty-two players, including John Daly in only his second PGA Tour event this year, were at even par or better.
World No. 1 Luke Donald, who has been second, third and second at the tournament the past three years, opened with 75. He has to finish in the top eight or he will surrender the top spot to No. 2 Rory McIlroy next week.
Donald had 11 consecutive rounds under par at Harbour Town before chopping it around Thursday. He made only one birdie.
Matt Kuchar was tied for the lead at Augusta National with three holes left before finishing two shots out of the playoff between Bubba Watson and Louis Oosthuizen, shot 72 on Thursday.
Campbell held a first-round lead for the first time since the 2009 Masters Tournament. His game has faded some since then – he recorded only one top 10 at the British Open last year, his fewest since coming out on tour in 2002 – and has missed five cuts in nine tournaments this year.
“I haven’t felt like I’ve been that far off,” Campbell said. “But the results haven’t been good at all.”
Campbell got it going quickly at Harbour Town with an 8-foot birdie putt on No. 2 and then consecutive birdies on the fourth and fifth holes. He moved to 4-under two holes later, rolling in a 20-footer for birdie.
Campbell added a final birdie on the 15th.
Campbell said the wind reminded him of his days playing golf in West Texas.
“Other than the trees and the ocean,” he joked.