
The 40-year-old Swede held off the challenge of the American to win in a record Open score of 20 under par, and he jumps above Bubba Watson to world number five.
Despite remaining without a win since his Open triumph in 2013, Mickelson leaps to 13th, his highest ranking since September 2014.
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Australian Jason Day retains his lead over Dustin Johnson as world number one, after both failed to contend at Royal Troon.
Spaniard Sergio Garcia picked up his 22nd top-10 finish in major tournaments, and moves back into the world’s top 10 for the first time in over a year.
World top 20 on July 18:
1. Jason Day (AUS) 13.24 pts
2. Dustin Johnson (USA) 11.29
3. Jordan Spieth (USA) 10.86
4. Rory McIlroy (NIR) 9.39
5. Henrik Stenson (SWE) 8.88 (+1)
6. Bubba Watson (USA) 7.10 (-1)
7. Rickie Fowler (USA) 6.56
8. Adam Scott (AUS) 6.40
9. Danny Willett (ENG) 6.23
10. Sergio Garcia (ESP) 5.58 (+2)
11. Justin Rose (ENG) 5.37
12. Branden Grace (RSA) 5.33 (-2)
13. Phil Mickelson (USA) 5.16 (+6)
14. Patrick Reed (USA) 5.00 (-1)
15. Louis Oosthuizen (RSA) 4.55 (-1)
16. J.B. Holmes (USA) 4.47 (+8)
17. Matt Kuchar (USA) 4.30 (-2)
18. Brooks Koepka (USA) 4.13 (-2)
19. Hideki Matsuyama (JPN) 4.13 (-2)
20. Zach Johnson (USA) 4.08 (-2)
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