For Horschel it was the fourth PGA title win of his career and he was delighted to overcome several bouts of nerves to take the victory.
He added of himself and Day, "I don't think either of us played spectacular today".
Par for the pair forced a playoff where Horschel would eventually make par again, Day had the chance to force a second playoff hole but would eventually 3 putt the 18 and hand the victory to Horschel.
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. He just missed an 18-foot birdie putt on the first playoff but won with a par as Day's four-footer slid past the hole to the left. "The nerves I can control - it's making the right decisions and just trying to judge the wind correctly and when to hit the ball, where to aim and the little things that kind of make up the difference between shooting 64 or 70". After Day missed a tough birdie putt, Horschel came just 4 inches short of draining his and walking off with a victory.
Horschel arrived at TPC Four Seasons Las Colinas in the middle of his worst run on the PGA Tour since his rookie season of 2011 when he missed 14 cuts in 25 starts. Day will go into Sunday's final round tied for third with Jason Kokrak at 10-under.
"I know that feeling", Horschel said about Day's unexpected playoff miss. "I won, and I don't want to leave". He is 2-for-2 in winning after holding the 54-hole lead at PGA Tour Champions majors. The third-ranked Jutanugarn, defending the first of her five tour victories previous year, had a 70 to also reach 4 under.
Andrew Landry (Arkansas Razorbacks) shot a 66 and is tied for fifth at 15 under.
Horschel admitted he had been struggling before this win, his first since the 2014 Tour Championship. Funk, who held a one-stroke lead after the second round, has 14-under 202 to maintain a one-stroke edge over Scott Parel (70) in the first of the tour's five majors.
Stephan Jaeger's two eagles lifted him to a 6-under 65 on Saturday and the lead at the BMW Charity Pro-Am at Greenville, S.C. He came to the house in 1-under, outpacing bogey-5s at 10 and 12 with birdies at 11, 15 and 16.
His three-day total of 19-under 195 is one stroke better than Andrew Yun, Xinjun Zhang and Tyler Duncan. Horschel won on the first playoff hole.