Woods, who snapped an 11-year major win drought at last month's Masters, opened with a double bogey at the par-4 10th hole and made another at the par-3 17th to reach the turn three-over par at the formidable, 7,549-yard, Bethpage Black.
Koepka, who played alongside Woods and British Open champion Francesco Molinari in the feature group, was spectacular, holing a 40-foot birdie putt at 10, sinking a 20-foot birdie putt at the par-3 14th and adding two more at 18 and one.
That left third-ranked Koepka sharing the lead with England's Tommy Fleetwood, trying to become the first Englishman to win the event since Jim Barnes in 1919.
Fleetwood opened with a bogey at 10, answered with birdies at 15 and 16 and birdied three of the first four holes after making the turn.
With a victory, Koepka would become the first player to own back-to-back titles at two majors at the same time.
"I like my chances this week," he said.
"I'm playing good. If I do what I'm supposed to do, then I think I'd be tough to beat."
Sixth-ranked Woods stumbled badly early alongside Koepka and Italy's Molinari at the first PGA Championship played in May since 1949, the event moving from August this year in a revamp of the global golf schedule.
From one of Bethpage's toughest tees, Woods missed the 10th fairway and found the rough, hit a layup then went over the green and chipped to six feet. But he lipped the right edge on his bogey putt to make double.
It was only the fourth time in 82 major starts that Woods began with a double bogey or worse, but the first time at a PGA. He opened with triple bogey at last year's US Open and began with a double bogey on his way to winning the 2008 US Open.
Woods made a 15-foot birdie putt at the par-4 15th, saved par at 16 with a 90-foot wedge shot to two feet but made double bogey at 17, finding a bunker and the fringe before three-putting. He answered with birdies at the first and second that pulled him to 1-over.
Molinari made bogeys on three of the first six holes but birdied two of the next three holes to make the turn on level par.
- Tiger hunts Snead, No.1 -
A victory would match Woods with Sam Snead for the all-time US PGA win record at 82 and move him two shy of the all-time major record of 18 set by Jack Nicklaus -- as well as put Woods halfway to a calendar Grand Slam for the first time since 2002.
The 43-year-old American superstar's electrifying triumph last month at Augusta National has made him the focus of attention on the same layout where he won the 2002 US Open.
Koepka held off Woods to win last year's PGA at Bellerive before Woods turned the tables at the Masters, completing an amazing comeback after 2017 spinal fusion surgery that ended years of back woes.
"It was great to see him win," Koepka said.
"I was a little bit disappointed. I felt like I let it slip a little bit. But at the same time, that's what our sport needed. We needed him to win a major."
Woods has not played competitively since the Masters, making this only the sixth time in his career he has played back-to-back majors.
Woods could become world number one for the first time since March 2013 by winning. He would need top-ranked Dustin Johnson to finish worse than solo 11th and neither Koepka nor world number two Justin Rose of England to finish second alone.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)