In his first appearance at East Lake Golf Club since 2013, Tiger got off to a shaky start, three-putting his first hole for the only bogey of his day. He battled back to 1-under at the turn, setting himself up for a remarkable back nine.
After two brilliant approach shots led to birdies on No. 12 and 14, Tiger finished his round in style, eagling the par-5 18th and celebrating with a massive fist pump.
This is the second straight event Woods has shared the 18-hole lead. He shot 62 at the BMW Championship two weeks ago.
Fowler missed the first two playoff events due to an oblique injury but showed no rust in carding his fourth 65 in his last five rounds played. He is searching for his first win this season.
Bryson DeChambeau held the FedEx Cup points lead heading into the Tour Championship, but a disappointing 71 in Round 1 projects him to relinquish the top spot.
Woods and Fowler will be in the final pairing when play continues at East Lake on Friday.