Mickelson posted a final round of 5-under-par 66 for a 72-hole total of 281 and a three-stroke victory at the 142nd Open. He was the only player under par for the tournament
Mickelson was eighth in the rankings prior to winning the Scottish Open July 14. That win improved his position three spots and Sunday's victory at Muirfield Golf Club lifts him another three places to second.
It was his fifth major tournament win. He previously won the Masters (2004, '06, '10) and the PGA Championship (2005). He needs the U.S. Open for the career Grand Slam. He's finished second six times, including this year, at that event.
Rory McIlroy, who missed the British Open cut, slips to third and Justin Rose goes from third to fifth. Brandt Snedeker is up one place to seventh, forcing Graeme McDowell down one spot to No. 8. Lee Westwood returns to the Top 10 at No. 10, up two places. Steve Stricker drops to 11th.
Woody Austin claimed his fourth PGA Tour win Sunday at the Sanderson Farms Championship. That moves him to 257th in the rankings, a jump from No. 608.
It was his first title since June 2007.
The men's world golf rankings Top 10 with player's name, home country, rankings point average and British Open finish:
1. Tiger Woods, United States, 12.64, tied for sixth
2. Phil Mickelson, United States, 8.63, first
3. Rory McIlroy, Northern Ireland, 8.61, missed cut
4. Adam Scott, Australia, 7.72, tied for third
5. Justin Rose, England, 7.71, missed cut
6. Matt Kuchar, United States, 6.54, tied for 15th
7. Brandt Snedeker, United States, 6.08, tied for 11th
8. Graeme McDowell, Northern Ireland, 6.07, tied for 58th
9. Luke Donald, England, 5.55, missed cut
10. Lee Westwood, England, 5.21, tied for third
Swim Week Miami Beach 2014 [PHOTOS]