Mickelson recovered from a 72nd-hole bogey by nearly holing a wedge shot and then tapping in for a birdie on the first playoff hole to beat Branden Grace. It was Mickelson's 50th professional win.
Eight of those are considered titles on the European Tour, although Mickelson's four major tournaments also fall into that designation.
He heads about 180 miles north from East Lothian, site of this year's Scottish Open, to Inverness and the British Open this week.
Jordan Spieth, who sank a shot from a bunker on the 72nd hole and then survived a three-way sudden-death playoff for five holes Sunday, became the youngest player to win a PGA Tour event since Ralph Guldahl won the Sana Monica Open in 1931. Spieth will turn 20 in two weeks.
Spieth had five birdies (and a bogey) over the last six holes of regulation. He, Zach Johnson and David Hearn tied for first but Spieth, with a par at the 18th on the fifth playoff hole, claimed the title.
He moves up 61 spots in the rankings to No. 59.
The men's world golf Top 10 rankings with player's name, home country and ranking points average:
1. Tiger Woods, United States, 12.37
2. Rory McIlroy, Northern Ireland, 8.79
3. Justin Rose, England, 7.82
4. Adam Scott, Australia, 7.07
5. Phil Mickelson, United States, 6.68
6. Matt Kuchar, United States, 6.47
7. Graeme McDowell, Northern Ireland, 6.12
8. Brandt Snedeker, United States, 5.93
9. Luke Donald, England, 5.68
10. Steve Stricker, United States, 4.96