Tiger reunion with ex-caddie spoiled at Open
Instead, 54-hole leader Adam Scott, who now has Williams as his bagman, will play alongside Northern Ireland's Graeme McDowell with 14-time major champion Woods in the penultimate pairing alongside fellow American Brandt Snedeker.
Woods, who fired Williams a year ago and now has Joe LaCava as his caddie, had been the target of insults from Williams last year, after Williams hooked up with Scott and quickly won a World Golf Championships event.
"I was very fortunate on the timing with Steve," Scott said. "We're getting on really well out there. He believes in the way I'm going about my business.
"And at some point tomorrow, I'm sure there's going to be a time when I'm going to lean on his experience and he's going to have some great advice for me on how to tackle a certain situation. And that's an advantage."
Williams, from New Zealand, apologised to Woods last year for his comments when they met at the Australian Open in Sydney and agreed to shake hands and move on.
Woods would not say if a potential final-pairing date with Scott and Williams was on his mind as he stood in second place on the back nine at Royal Lytham before a late bogey and birdies by Snedeker and McDowell doomed the bid.
"Final pairing, whatever it may be, I was just trying to cut into the lead," said Woods, who when asked if he would have wanted to be in the last group replied, "Well, I'm not. So it is what it is."
Scott, who leads Snedeker and McDowell by four strokes and Woods by five in quest of his first major title, said he would not have minded having Woods alongside him in the final group.
"It wouldn't bother me," Scott said. "I've played with him a lot. I don't think it would have bothered me at all. I would have been happy. I'm just happy to be in this position. To be honest, I'm really excited about tomorrow."
Woods says Scott is overdue to make his mark as a major champion.
"He has been out here a long time," Woods said. "I don't think he has really done probably as well as he would like to in major championships. But he's maturing in his game and over the last year or so he has really improved.
"Adam is in a great spot right now. He has got a four-shot lead and he's playing really well."
Woods has himself in the hunt for a 15th career major title, which would put him only three shy of the record 18 majors won by Jack Nicklaus.
But Woods has not won a major since the 2008 US Open and the 2009 revelation of his secret sex life. He was a 36-hole co-leader at the US Open last month only to fire a third-round 75 and stumble off the pace.
Woods made four bogeys in the first eight holes in his third round at the US Open last month and started poorly on Saturday at Royal Lytham as well, missing par putts of eight feet and the first and 10 feet at the third.
Woods rammed in a 40-foot birdie putt at the sixth hole, added a tap-in birdie at the par-5 seventh and birdied the par-3 ninth to pull level with Snedeker.
"Considering I got off to such a bad start, I figured if I could get to one-over or even through the turn, that would have been positive going into the back nine. I actually happened to turn at 1-under, which was a bonus.
"I turned it around. I got off to an awful start and battled back and got myself right back in the mix again. I'm right there."
Brisk winds are in Sunday's forecast but Woods is mostly concerned with himself.
"I've just got to execute my game plan," Woods said. "Whether the wind blows or not, I've still got to go out there and post the round I know I need to post and execute my plan."