Johnson fired a six-under par 66 to share the lead with US PGA Tour rookie Kevin Na and Matt Kuchar on eight-under par 136 after two rounds of the $9.5 million event at TPC Sawgrass.
Woods, a 14-time major champion chasing the record 18 major titles won by Jack Nicklaus, avoided what would have been the first back-to-back missed cuts of his pro career by firing a 68 to stand on two-under 142.
“I probably could have gotten one or two more out of it but I really played well,” Woods said. “I was just very consistent, nothing spectacular, just real solid golf.”
Woods sank four birdies in a row starting at the par-3 eighth, including birdies at the par-5 ninth and 11th holes, to finish in a share of 30th among 72 players who made the cut on level par 144.
“I’m still with a good chance,” Woods said. Missing for the weekend will be Northern Ireland star McIlroy, who defends his US Open crown next month at San Francisco.
Last week, McIlroy lost in a playoff at Quail Hollow. This week, McIlroy opened with a 72, then followed with a 76 to miss the cut for the first time in more than a year. McIlroy has missed the cut in all three of his Players starts.
Johnson birdied three of the first four holes, took a bogey at the par-4 seventh, then opened the back nine with four birdies in the first five holes. He added a birdie at the par-5 16th but closed with a bogey.