Back-to-back birdies at the 14th and 15th holes, followed by a further two in succession at the 17th and 18th, helped Horschel to a flawless seven-under-par 63 and a three-stroke lead in Colorado on Saturday.
The American - 20th in the FedEx Cup standings and projected to top the rankings should he win the third play-off event - is clear of compatriot Ryan Palmer at 13 under through 54 holes at the Cherry Hills Country Club.
Palmer had six birdies and three bogeys as he shot a third-round 67 to be three shots off the pace.
The three-time PGA Tour winner was 37th in the rankings and set to miss the 30-man cut for the season-ending Tour Championship prior to the opening round, but he is now projected to climb 28 positions to ninth.
German Martin Kaymer and American Bubba Watson are tied for third at eight under heading into the final round.
Kaymer had a bogey-free back nine, which included three consecutive birdies starting at the 10th hole, as he fired a six-under-par 64.
Watson holed back-to-back birdies at the 16th and 17th for a 66 on day three.
American Rickie Fowler (66) has sole possession of fifth spot at seven under for the tournament.
Sergio Garcia surrendered his lead after shooting a two-over-par 72, which included three bogeys.
The Spaniard is now seven shots off the pace in sixth spot.
American pair Jim Furyk (67) and Jordan Spieth (68), and Canadian Graham DeLaet (69) are level at five under.
World number one Rory McIlroy and Adam Scott headline a group of five players nine shots off the lead.
A triple bogey at the par-three 12th hole capped a forgettable day for Northern Irishman McIlroy, who went two over after consecutive 67s from his opening two rounds.
Australian Scott fared slightly better despite sinking two bogeys and a double bogey on Saturday, carding five birdies for a 69.
American trio JB Holmes (67), Morgan Hoffman (62) and Chesson Hadley (68) are also four under.