Woods, a 14-time major victor in the eighth month of his comeback from spinal fusion surgery, opened Saturday with a birdie at the par-5 eighth.
Woodland shot a second-round 66 to reach 10 under.
Englishman Matt Wallace popped up onto the PGA Championship third round leaderboard in spectacular style on Saturday, carding an ace at the 232-yard, par three 16th.
His nearest challenger is former Masters victor Adam Scott of Australia, who carded a fine five-under 65 for 10-under 200, two shots back.
The 42-year-old former world number one finished off the last 11 holes of a storm-halted second-round 66 Saturday morning, then delighted thousands of spectators following his every shot with a sizzling afternoon start.
"I thought I played really clean cards, really clean rounds", said Woods, who made eight birdies and three bogeys over the course of the two rounds.
"I mean, it would be more-than-twice the thrill for me", he said, "but no matter who wins tomorrow, if that person has met Jarrod, they will have felt something with him passing this week".
Bellerive was playing shorter Friday than for the opening round.
Woods failed to convert on both, despite having given himself excellent chances. Bryson DeChambeau three-putted his final hole, missing a 4-foot par putt on No. 9, to miss the cut by one shot.
"I get it all the time, so I'm used to it by now".
"If you hit the ball in the right spots on the greens, there's not a single putt out here that you are afraid of, " he said. "They were talking about him as we left and I was just standing there laughing. And I blew it by 4 feet and then pulled the next one". "It was a long day".
And you know what the philosophy has produced this week at the PGA? "It was a long day". Joining Koepka in Sunday's final pairing, at 1:55 p.m. local time, the Aussie is 10 years older than Koepka and is still similarly the physical specimen.
Johnson also missed a 10-footer for birdie at the sixth.
Resuming his weather-delayed round on the 12th hole Saturday, the Lehi resident made two more birdies and two bogeys to finish.
At four shots back in a six-way tie, there's a cosmopolitan group including Irishman Shane Lowry, Aussie Jason Day, defending champion Justin Thomas - and Tiger.
The South African said he suspected there was a low round out there for the taking and minutes after Koepka notched his 63, Schwartzel became the 16th golfer to shoot the score at the season's fourth major. "St. Louis has never seen Tiger up close, so it's pretty insane and it makes it a lot more fun". Hearing the crowd, and Tiger's performing great. He was helped by a marvellous stroke at the 14th where he pitched in from the back of the green, but the abiding moment was he flew the putting surface once more with a wedge in his hands.
In the third round, Finau made four birdies and three bogeys.
And the round was solid, perhaps something to build on. But he needed 18 putts on the back nine for a total of 30, and the difference between being closer to the lead. But there's no question what Woods will need to do.
"Not just myself, but everyone's going to have to shoot low rounds, " Woods said. Look at that front nine.
The St. Louis fans, who have proven so far this week that they root for birdies of more than just the Cardinal type, should get a much better finale Sunday.