Thompson is 13-under on Sea Island’s Seaside Course. Horschel followed his opening 64s with 70.
Simpson shot 69 and is tied with 2008 Masters Tournament champion Trevor Immelman, who matched the course record of 62, at 11-under. Simpson and top-ranked Luke Donald are vying for the money title and both will play next week in the season finale at Disney. Simpson trails Donald by $68,971, but could move into the top spot with a strong round Sunday.
Simpson also is looking for a tour-leading third win this year, which could make him the favorite for PGA Tour player of the year.
CHAMPIONS TOUR: In San Antonio, Fred Couples birdied six of the first seven holes and finished with a course-record 10-under 62 to take a seven-stroke lead in the AT&T Championship.
Couples had 12 birdies – six in a back-nine 30 – and a double bogey to reach 17- under at TPC San Antonio’s Canyons Course, the first-year venue after nine years at Oak Hills.
Mark Calcavecchia is second after a bogey-free 66. He made a 20-foot birdie putt on the 18th.
The seven-stroke lead is the largest 36-hole margin on the tour since 1998.
LPGA TOUR: In Kuala Lumpur, Malaysia, South Korea’s Na Yeon Choi took a one-stroke lead over Brittany Lang in the LPGA Malaysia, finishing off a 4-under 67 after a rain delay.
Choi birdied the par-3 15th and par-4 16th and closed with two pars to reach 12- under at Kuala Lumpur Golf and Country Club. Lang, tied for the second-round lead with fellow American Stacy Lewis, birdied four of the last six holes – the last on the par-4 18th at dusk – for 69.
Spain’s Azahara Munuz is 10-under after 68. Yani Tseng, a six-time LPGA Tour winner this season, had 69 to match Lewis (72) and Se Ri Pak (65) at 8-under.
EUROPEAN TOUR: In Vilamoura, Portugal, Rafael Cabrera-Bello, of Spain, shot 8-under 64 to take a one-shot lead into the final round of the Portugal Masters.
Cabrera-Bello had two eagles and five birdies, leaving him at 18-under 198 at Oceanico Victoria.
NATIONWIDE TOUR: In Miami, Jason Krokak shot 2-under 69 to take a three-shot lead over Matt Every in the Miccosukee Championship.
Krokak is at 15-under 198 at Miccosukee Golf and Country Club.
Aiken’s Matt Hendrix shot 69 and is tied for seventh at 204. Former Augusta State star Major Manning (75) is tied for 66th at 214.