Horschel came into the tournament having missed four consecutive cuts but turned his fortunes around with some incredible putting at the TPC Four Seasons resort near Dallas.
Australia's Day missed a short putt on the 18th hole that would have extended the playoff to hand Horschel the victory.
"That's not the way I wanted to win it," said Horschel. "Four missed cuts to come in here and I played this well -- someone is looking out for me."
Both Horschel and Day finished 72 holes on 12-under par 269. Day fired a two-under 68 Sunday while Horschel shot 69, each finishing one stroke ahead of American James Hahn, who was third after shooing 71.
American Jason Kokrak finished fourth on 270.
Horschel had the top putting percentage in the players in the field while world number four Day had made 95 percent of his putts inside five feet this season before missing what appeared to be a routine four-footer to drop the playoff.
Day, Horschel and Hahn all played in the final group, creating a bit of a match-play scenario.
Horschel's two-putt birdie on the par-5 16th moved him back into a tie for the lead with Day while Hahn's par on the hole all but ended his chances. Both Day and Horschel parred 17 and 18.
Danny Lee of New Zealand (68), American Sean O'Hair (68), An Byeong-Hun of South Korea (69) and Amrican Bud Cauley (70) shared fifth on 272.
Canada's Nick Taylor (65), Joel Dahmen (67), Matt Kuchar (69) and Cameron Tringale (72) were another stoke back.
World number one Dustin Johnson never made a serious run and finished tied for 13th at 274.
Defending champion Sergio Garcia, who won his firts major title last month at the Masters, shot 74, the Spaniard finishing in a tie for 20th on 276.
source: news.abs-cbn.com
