GULLANE, Scotland—Lee Westwood finished the British Open's third round Saturday with a two-stroke lead over Tiger Woods and Hunter Mahan. But there was a moment late in the round at Muirfield when the cosmic momentum seemed to be swinging Woods's way. That it didn't is the difference between the world now and the world back when it belonged to Woods and all of golf's other best players just lived in it.

Lee Westwood on the 16th green on Saturday. Associated Press

Westwood, leading the tournament by a shot over Woods and playing with him, pulled his tee shot on the par-three 16th into the deep gunch left of the green. With a big swing of his wedge, he barely managed to plop the ball onto the bank of the green and watched it meekly roll down into a hollow.

He then putted up the slope but left himself 18 feet for a bogey. A double bogey seemed likely.

Woods, meanwhile, had driven ideally into the middle of the green. He had 20 feet, uphill, for birdie. Back in the day, this was the type of putt he never seemed to miss. When blood was in the water, he attacked.

But Woods's putt curled harmlessly left of the cup, and Westwood popped his bogey effort into the center of the cup. What could have been a three-shot swing in Wood's direction became instead merely a one-shot bobble for Westwood.

And Westwood swung things back the other way on the next hole, the par-five 17th. After Woods hit his second shot into a fairway bunker, and punched out, he found himself staring at a 12-foot putt for par. He missed, and Westwood followed immediately with a 10-foot putt, on the same line, for a birdie.

Presto: Westwood, not Woods, was now two up, and that is where the day ended. More important, he claimed pole position for Sunday's final round. Woods has never won a major coming from behind.

"That was probably the biggest momentum thing I did all day, walk off [No. 16] with a bogey," Westwood said afterward.

It definitely turned the fans ringing the final holes in Westwood's favor. Granted, this is the British Open and Westwood is a Brit, but Woods is still golf's reigning deity and is usually worshiped when he strides onto greens. On Friday, however, Woods's walk onto the 17th garnered scant reaction from the crowd. Westwood, on the other hand, received huge applause. The shouts of "Go on, Lee" outnumbered cries of "Let's go, Tiger" by about 4 to 1. After Tiger's miss on No. 17 and Westwood's birdie, the Englishman received his biggest cheer of the round.

Woods and Westwood started Saturday a shot behind Miguel Angel Jimenez, and played in the next-to-last group behind Jimenez and Henrik Stenson, who shot 74. But the seesaw battle between Woods and Westwood was story of the day.

Woods led Westwood by two shots by the third hole. But Westwood curled home a 45-foot eagle putt on the fifth, which Tiger bogeyed, to claim solo first for himself. He briefly stretched his lead over Woods and the field to three with a birdie at seven. But bogeys on the next two holes, and a birdie by Woods at nine, tied them up. Westwood went ahead by a shot again with a birdie on 14, where they were when they reached the 16th.

Jimenez, the 49-year-old first-round leader from Spain, faded from the start. He suffered four bogeys in his first eight holes and finished with a 77, three over par for the tournament and now six behind the lead.

Westwood was the only player to break par out of the nine who started Saturday's round within two strokes of the lead. One of those would-be contenders, Martin Laird of Scotland, the home fans' hope even though he now lives in the U.S., shot 81.

On Sunday Westwood will be paired with Mahan, whose was one of three players Saturday to shoot 68 (five birdies, two bogeys). The others were Sergio Garcia and Richard Sterne. Altogether, 12 players broke par.

In general, Muirfield played easier Saturday than it did in the first two rounds. "They put a lot more water on it, and the greens were a little bit slower," said Ernie Els (70 and five over par). The winds were mild by Scottish coastal standards, just five to 10 miles an hour through most of the day, and Sunday's forecast calls for more of the same.

The bigger prognostic question is how well Westwood will hold up. He holds the unofficial title of best player never to have won a major championship, and, at 40 years old, he knows that opportunities are dwindling.

"Even though I haven't won a Major, I know what it takes to win one," he said. "It's just a case of going out there tomorrow and having the confidence in my game, which I've got. And putting it to the test."

He said that he isn't feeling much pressure. "I figured if I was going to win this tournament, I was going to have to beat Tiger," he said. "It generally works like that, whatever tournament you're playing in that he's playing in."

Woods will be playing ahead of Westwood, with Adam Scott, who shot 70 Saturday and stands at even par. If Woods gets on a roll, Westwood will know it, and hear it.

But as Woods pointed out, it isn't a two-man tournament. In addition to Mahan and Scott, major champions Zach Johnson and Angel Cabrera are still in the mix. They are among four players just four off the lead. Phil Mickelson is five back.

On a dangerous Muirfield course that R&A officials will probably set up tougher and firmer than it did on Saturday, Westwood's two shot lead is anything but comfortable.

—Joshua Robinson contributed to this article.

Corrections & Amplifications
The third round of the British Open concluded on Saturday. A previous version of this article misstated it as the second round.