Xander Schauffele and Canadian Nick Taylor were both four strokes behind Clark, who was on 14-under par 130 after 36 holes at TPC Sawgrass, but world number two Rory McIlroy fell back after shooting a one-over 73.
World number one Scottie Scheffler battled a neck injury but stayed in contention with a 69 that left him six strokes back.
But Clark will take some beating if he can maintain the levels he has shown with his game over the past two days as he chases down the $4.5 million winner's purse at the US PGA Tour event at Ponte Vedra Beach, Florida.
The 30-year-old American has risen from outside the top 100 in the world rankings a year ago to sitting in fifth place heading into this tournament.
He announced his arrival with victory at the Wells Fargo Championship last May and then followed up a month later with his triumph at the US Open at Los Angeles Country Club.
Last month, he added a victory at Pebble Beach, another of the tour's "signature" tournaments, to his resume and now has his eyes set on what was once considered golf's 'fifth major.'
His 130 for the opening two rounds is the second-lowest midway total in Players history and his final nine holes on Friday, on the front side, started with four straight birdies and ended with another on the par-5 ninth.
Highlights were an 18-foot birdie putts at the sixth after a 22-footer to save par on the previous hole.
Clark, who finished second at Bay Hill last week, rejected the idea that he only truly zones in when it matters most.
"I just really don't know what it is," he said. "I would like to play great every week. I really looked at how Scottie (Scheffler) has been playing this year and last year and I use him as someone to try to keep up with and he plays good every week.
"So my thing is just try to be consistent and with our schedule now too, you kind of only play big events, so that's part of it as well."
Schauffele's push could have been undone by a double bogey when he found water on the par-5 11th but he bounced back with an eagle on the 16th, where a superb fairway shot left him with a nine-footer.
"It was just a terrible swing. Was a bit uneasy," he said of the double bogey.
"I watched two great shots into that green and thought I could pile one on there and sort of cut the lead even more, and to go backwards on a par-5 is never what we're trying to do. Then compounding a terrible wedge shot on top of it. So happy to birdie the next and a bonus to make the eagle on 16."
Taylor's 68 featured three bogeys but he stayed within distance of the lead thanks to birdies on 15 and 16 following superb approach shots.
Scheffler struggles on
Scheffler had to receive attention from a PGA Tour physiotherapist.
"I hit a shot on my second hole today and I felt a little something in my neck, and then I tried to hit my tee shot on 12, and that's when I could barely get the club back," he said.
"I got some treatment, maybe it loosened up a tiny bit, but most of the day I was pretty much labouring to get the club somehow away from me.
"I did enough I felt like to keep myself somewhat in the tournament, and so that's really all I could ask for. The way I was getting around the course, the way my neck was feeling, I didn't know if I was going to be able to continue playing."
The prospect of a pre-Masters boost for McIlroy quickly faded. The Northern Irishman made three bogeys and three birdies on his first six holes but made a double bogey on the par-4 14th to drop back.