Atlanta, who won the first match of the best-of-three final on Monday, slipped 3-0 behind after failing to win any of the first 11 holes.
They narrowed that gap to 3-2 after 13 before dropping the hammer, which made the penultimate hole worth two points.
And Horschel glided across the green after holing an 18-foot downhill putt that edged his side ahead.
“I hit the spot, it looked good. Two feet out I knew it was in the hole and I blacked out,” Horschel said.
“I think I said some expletives. I think I said something about this being my house. It was a lot of fun.”
New York dropped the hammer for the final hole to try and snatch the game but after both players missed the green, Cantlay’s delicate pitch landed within a foot of the hole to seal the win.
The innovative technology-led indoor tournament was founded Tiger Woods and Rory McIlroy, who said they wanted to help take golf “into the 21st century”.
“It’s completely exceeded my expectations,” said two-time major winner Thomas. “The competitiveness, once the play-offs got here, it was not chippy, but it was competitive. We wanted to win.”
