Woods, in the eighth month of his comeback from spinal fusion surgery, ran off three birdies in four holes Friday to stand 3-under through seven holes for the event when storms stopped play Friday at Bellerive Country Club.
Johnson and Belgium's Pieters are level with Schwartzel after carding 66s.
And then Charl Schwartzel made it 16 players with his eight-birdie round of 63.
"I feel safe because I feel safe where my game is", Woodland said.
Defending champion Justin Thomas stayed in the game, and so did Tiger Woods.
"I'm in a lot better position than I was when I came out here this morning, which is great", Thomas said.
After a par at the fourth, Woods hit a booming 318-yard drive into the fairway at No. 5, then stuck an approach shot to inside of 10 feet.
"They key is to get the ball in the fairway and attack from there", Woodland said. "I just didn't make any putts".
With leaders Gary Woodland, Kevin Kisner and Brooks Koepka going ultra-low earlier in the day on Friday, Woods teed off in the afternoon needing to post a low score to keep in touch with the large group of players at 5-under par or better. The third round featured threesomes off both tees, meaning close to five-hour rounds on a course that feels even longer to walk because of the soggy conditions. Bryson DeChambeau three-putted his final hole, missing a 4-foot par putt on No. 9, to miss the cut by one shot.
"It's always a bit frustrating to have to come back and finish a round in the morning, but that's golf, and something I will just have to deal with", Fox said after his truncated round.
It's the 34th and 35th time a player has shot 63 in a major championship and the first since Tommy Fleetwood did it in the final round of this year's U.S. Open at Shinnecock. They have also finished their first two rounds. Mickelson is still expected to be one of captain Jim Furyk's four at-large picks, with three coming on September 4 and the final one coming on September 10. Finau opened with five straight birdies, only to hit into the water and make triple bogey on No. 6.
After opening his day with a gain at the par-five eighth he dropped back to two-under with an immediate bogey at the next but a flawless back nine, including a late birdie at the par-five 17th moved him into contention.
Jim Furyk will get four captain's picks on September 4, and Mickelson stands a good chance of being one of them.