"I don't want to win like that," Horschel said after his first victory since 2014.
The win marked a major turnaround for the American, who had missed four consecutive cuts entering play at TPC Four Seasons.
"Four missed cuts to come in here and I played this well -- someone is looking out for me," Horschel said.
They had ended on 12-under-par 268 in regulation. Day shot 68 for the round and Horschel 69.
Both players missed par putts on the last hole to force the playoff.
Horschel made the turn at even par after a bogey at the ninth hole, while Day was one-under.
Both bogied the 12th with Horschel adding another bogey at 13 before draining a 60-foot birdie putt at 14 for a share of the lead.
Day responded by chipping in from 26 yards to birdie 15.
A birdie by Horschel on 16 helped set the stage for a playoff as both parred the final two holes.
Overnight leader James Hahn finished one stroke back at 11-under 269 after a 71 and fellow American Jason Kokrak was another stroke back.
World number one Dustin Johnson tied for 13th at 6 under after a final round 69.
The tournament was the 35th and last at TPC Four Seasons in Irving, Texas. It will move to Trinty Forest Golf Club near Dallas.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Greg Stutchbury/Peter Rutherford)
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