Mickelson had not been at his best in previous British Opens. In 19 appearances, he had recorded only two Top 10s.
This time, because of a final-round five-under 66, he won by three strokes over Henrik Stenson. Lee Westwood, who was the leader heading into Sunday, faltered with a 75 to finish four back.
The victory put Mickelson closer to the career grand slam. At 51, he has yet to achieve it.
2016: Royal Troon Golf Club, Scotland
As in 1977, it was a two-man battle. Mickelson, seeking his second British Open, was on fire from the start, with rounds of 63, 69, 70 and 65. Stenson was better, setting a record for the fewest strokes, 264, in a major championship.
They were tied with five holes to go on Sunday. Stenson, who shot a final-round 63, birdied 14, 15 and 16. At 15, he made a 51-foot putt from off the green. J.B. Holmes finished third, 14 back.