With four birdies over the last six holes, Mickelson closed with a 5-under 66 for a three-shot win over Henrik Stenson.
No longer is he mystified by links golf, and he has his name etched in that jug to prove it.
"This is such an accomplishment for me because I just never knew if I'd be able to develop the game to play links golf effectively," Mickelson said. "To play the best round arguably of my career, to putt better than I've ever putted, to shoot the round of my life ... it feels amazing to win the claret jug."
Introduced as the "champion golfer of the year," he held the oldest trophy in golf over his head to show it off to one side of the massive grandstand lining the 18th green at Muirfield, and then the other. An hour earlier, they gave the 43-year-old Mickelson the loudest ovation of the week as he walked up the final fairway.
He drained an 8-foot birdie putt and thrust his arms in the air, hugged caddie Jim "Bones" Mackay and whispered to him, "I did it." After signing for the lowest final round ever at Muirfield, Mickelson huddled with his wife and three children back from a quick holiday to Spain for a long embrace and waited for the others to finish.
Westwood, who started the day with a two-shot lead, fell behind for the first time all day with a bogey on the par-3 13th hole and never recovered, closing with a 75.
Scott took the outright lead with a 4-foot birdie on the 11th, and then closed as sloppily as he did last year when he threw away the Open at Royal Lytham & St. Annes. He made four straight bogeys starting at the 13th, and a final bogey on the 18th gave him a 72. At least he has a green jacket from the Master to console him.
Woods, in his best position to win a major since the crisis in his personal life, stumbled badly on his way to a 74 and was never a serious challenger.
"We know that he goes for broke, and if that's how he was feeling and pulling it off, he's got the ability to do that," Scott said about Mickelson. "And he's gone and won an Open easily. So every credit to him."
At the end of a rough-and-tumble week along the Firth of Forth, Mickelson was the only player under par at 3-under 283. In his four other majors three Masters and one PGA Championship he had never started the final round more than one shot behind.
"I don't care either way how I got this trophy I got it," Mickelson said. "And it just so happened to be with one of the best rounds of my career, which is really the way I've played my entire career. I've always tried to go out and get it. I don't want anybody to hand it to me. I want to go out and get it. And today, I did."
Westwood, whose only other 54-hole lead in a major ended with Mickelson winning the Masters, paid tribute to Lefty for what will go down as one of the great closing rounds in a major.
"When you birdie four of the last six of a round any day, that's good going," Westwood said. "With a decent breeze blowing and some tough flags out there, it's obviously a pretty good experience. When you do it in a major championship, it's an even better experience."
But this major? Phil Mickelson?
He had only contended twice in two decades at golf's oldest championship. One week after he won the Scottish Open in a playoff on the links-styled course of Castle Stuart, Mickelson was simply magical on the back nine of a brown, brittle Muirfield course.
Tied for the lead, Mickelson smashed a 3-wood onto the green at the par-5 17th to about 25 feet for a two-putt birdie, and finished in style with a 10-foot birdie putt on the 18th.