There are only four major championships a year, so to play in 61, a golfing career must be long and — at least in some way — distinguished because they don’t just fling open the doors and welcome all comers. Lee Westwood first tried this task in 1995, when he was 22 and he qualified for the British Open at St. Andrews. He is 40 now, a father and husband and longtime professional — as they say here, a class player — who keeps coming back, keeps smiling at the opportunity even as so many have inflicted so much pain.

On Saturday night, in the midst of his 62nd major, Westwood could head off to dinner — pasta to recuperate the energy lost over a day spent on the maddening links of Muirfield — and then put his head on his pillow, allowing himself to dream one more time.

“I’ll think about winning the Open Championship tonight at some stage, I’m sure,” Westwood said. “I don’t see anything wrong with that — picture yourself holding the claret jug at the final green and seeing your name at the top of the leader board.”

It remains a fantasy right now despite all the fine work Westwood has done to put himself in this position. On Saturday, he outdueled Tiger Woods in what at times felt like a match-play event, scratching his way to a 1-under-par 70 that leaves him 3 under after 54 holes of the British Open. He is two shots clear of American Hunter Mahan and Woods, who has 14 major titles to his credit, second all time, but none since 2008.

Throw in other major winners near the top — Masters champ Adam Scott at even par, Angel Cabrera and Zach Johnson among those at 1 over, Phil Mickelson another shot back — and Sunday could be classic.

So the pressure, Lee. What about the pressure?

“Actually, I’m not in a high-pressure situation,” Westwood said, “because I’m going to go have dinner, and I’m so good with a knife and fork now that I don’t feel any pressure at all.”

This is how he has decided to handle it, with jokes and smiles and by balancing the importance of the opportunity with the knowledge that even a slight mishap could mean another chance slides away. “Not the end of the world if it doesn’t” happen, he said, and he smiled.

Starting with a third-place finish at the 2008 U.S. Open at Torrey Pines — a shot out of the epic playoff between an ailing Woods and an out-of-nowhere Rocco Mediate — Westwood has posted seven top-three finishes in majors, been ranked No. 1 in the world, missed a playoff in the 2009 British at Turnberry when he three-putted the final green and led the 2010 Masters after 54 holes.

“Even though I haven’t won a major, I know what it takes to win one,” Westwood 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.”

That test: Contain himself and master Muirfield. The rest of the field is another matter, out of Westwood’s control but very much a factor.

Start, of course, with Woods. He and Westwood began the day at 2 under, one off the lead of Spain’s Miguel Angel Jimenez, who slipped back badly with a 77. Westwood and Woods traded blows. Woods held the lead alone after he birdied the second; Westwood took sole possession when he rolled in an eagle putt from off the green at the par-5 fifth and eventually built a three-shot advantage; Woods got back to square when he birdied the par-5 ninth and Westwood responded with his second straight bogey. They fought.

And then two key moments on the back side: At the par-3 16th, Westwood hit his tee shot left into the high-as-your-thigh grass, came up with a nasty lie, hacked it out, watched it roll back to his feet and hit a poor chip. But the 20-footer he made to salvage bogey was, in his estimation, “probably the biggest momentum thing I did all day.” He and Woods shared the lead at 2 under.

Then, as Westwood was on his way to birdieing the par-5 17th, Woods made a crucial error. He had 238 yards to clear a bunker on his second shot. “If I hit it flat and flush, it’s fine,” he said. He didn’t, and when the ball found the bunker, birdie opportunity became bogey, and Woods finished with 72, falling out of the final group Sunday.

“I’ve got 14 of these things, and I know what it takes to win it,” Woods said. “He’s won tournaments all over the world. He knows how to win golf tournaments. He’s two shots ahead, and we’re going to go out there and both compete and play. And it’s not just us two.”

That is a salient point, not least because precisely zero of Woods’s major titles have come when he trailed entering the final round. So pay attention to Mahan, who played in the final group Sunday at this year’s U.S. Open and tied for fourth. His 68 on Saturday tied for the best round of the day and featured a gutsy, par-saving putt of 18 feet at the last. He will play Sunday with Westwood, thinking many of the same thoughts.

“You kind of have to believe before you can win,” Mahan said. “You’ve got to have that confidence knowing that ‘I can play well and I can win a major.’ ”

Scott has it because he turned last year’s fall-on-the-sword loss in the British Open — in which he bogeyed the final four holes — into victory at the Masters.

“It’s completely different,” Scott said after his third-round 70. “I think I go out there tomorrow not carrying the weight of the lead or not having won a major.”

That weight, then, would fall to Westwood. As he considered that afterward, he made it clear: While a victory could define his career, a loss won’t, and damn what other people think anyway.

“I don’t really live my life outside-in,” he said. “I don’t live it and run it according to what other people think. . . . I have my own ideas and my own dreams and my own plans.”

By now, they are well-stated, clearly envisioned. The only thing that remains is carrying them out.