Jonathan Coachman breaks down Phil Mickelson's 67-event winless streak and reviews Mickelson's history of coming up just short in major tournaments. (0:42)

TROON, Scotland -- Henrik Stenson kept hitting the best shots of his life, one after another, because there was no other way to beat Phil Mickelson in an Open showdown that ranked among the best in golf.

Stenson shot an 8-under 63 on Sunday to finish the tournament at 20-under and claim his first major championship. He won Sunday's matchup with Mickelson by 2 strokes and the Claret Jug by 3 over the American.

Stenson's final stroke of this major masterpiece was a 20-foot birdie putt on the 18th hole at Royal Troon that tumbled into the cup on the final turn. His 63 matched Johnny Miller for the lowest closing round by a major champion.

"I didn't know until they told me in the recorder's hut," Stenson said when asked if he knew that last putt was for 63.

Both Stenson and Mickelson played stellar golf, combining for an eagle, 14 birdies and two bogeys in the final pairing.

"Thank you very much for a great fight," Stenson told Mickelson as he accepted the Claret Jug.

Stenson ended his winner's speech on the 18th green by dedicating the victory to a close friend who died of cancer the day before The Open started.

"I feel like he has been with me all week. Mike, this one is for you," said an emotional Stenson as he raised the Claret Jug one more time and kissed it.

Mike Gerbich was a pal of the Stenson and his wife Emma when they lived in Dubai. Gerbich and Henrik Stenson used to play golf together.

"I know he's hurting inside," Stenson's caddie Gareth Lord said. "It's a perfect way to say thanks."

Henrik Stenson's outstanding round Sunday at The Open earned him the Claret Jug. Warren Little/R&A/R&A via Getty Images

Stenson delivered a crushing blow to Mickelson's chances of capturing a sixth major championship by making a 50-foot birdie putt from off the green at No. 15 that gave him a 2-shot lead with three to play. It was the first time all day the final group had been separated by more than 1 stroke.

The 40-year-old Stenson started walking when the putt was halfway there, stopping to pump his fist, rare emotion for the Swede with ice-blue eyes.

Life Begins at 40 With the victory Sunday, Henrik Stenson became the ninth golfer to win his first major at age 40 or older. Oldest players to win first major Golfer Age Event Jerry Barber 45 1961 PGA Roberto Di Vicenzo 44 1967 Open Darren Clarke 42 2011 Open Tom Kite 42 1992 U.S. Open Tommy Bolt 42 1958 U.S. Open Mark O'Meara 41 1998 Masters Reg Whitcombe 40 1938 Open Old Tom Morris 40 1861 Open Henrik Stenson 40 2016 Open -- ESPN Stats & Information

Mickelson narrowly missed an eagle putt on the 16th hole, and Stenson kept his 2-shot lead with an up-and-down for birdie from the deep rough.

"I knew he wasn't going to back down at any point, and in a way that makes it easier for myself," Stenson said. "I knew I had to keep on pushing, keep on giving myself birdie chances. He wasn't going to give it to me, so I had to pull away. I'm just delighted I managed to do that with a couple of birdies at the right time."

Mickelson led only once, a two-shot swing on the opening hole. They were tied with five holes to play until Stenson made an 18-foot birdie on the par-3 14th and then buried Lefty with a putt that defined his moment as a major champion.

J.B. Holmes finished third. He was 14 shots behind.

"Those guys are playing a different golf course than everyone else," Holmes said.

Stenson's previous best finish in a major was a tie for second at the 2013 Open at Muirfield, which Mickelson won for his most recent major victory.

He gave Sweden a long-awaited major in men's golf, 19 years after Jesper Parnevik lost a 54-hole lead at Royal Troon. Stenson said Parnevik sent him a message that said, "Go out and finish what I didn't manage to finish."

"I'm really proud to have done that, and it's going to be massive for golf in Sweden with this win," Stenson said.

Stenson's total of 264 set a record for lowest score at a major. Stenson eclipsed the Open mark of 267 set by Greg Norman at Royal St. George's in 1993 and the overall mark of 265 by David Toms at the 2001 PGA Championship. Stenson also tied Jason Day's record for lowest score under par set last year at the PGA Championship.

"It's disappointing to come in second, but I'm happy for Henrik," Mickelson said. "I've always thought that he is one of the best ball strikers in the game and that major championships are perfectly suited for him. I knew that he would ultimately come through and win. I'm happy that he did. I'm disappointed that it was at my expense."

For Mickelson, it's an 11th runner-up finish at a major in his career. Only Jack Nicklaus, with 19, has more second-place results.

"It's probably the best I've played and not won," Mickelson said. "That's probably why it's disappointing in that I don't have a point where I can look back and say, 'I should have done that' or 'Had I only done this.' I played a bogey-free round of 65 on the final round of a major. Usually that's good enough to do it. And I got beat. I got beat by 10 birdies."

The Associated Press contributed to this report.