The Australian sank a birdie on the second hole of the play-off to secure victory over the LPGA Tour. The Champions Tour team came last.
Day was joined by Nick Watney and Davis Love III in the US PGA Tour's line-up, while Cristie Kerr and Natalie Gulbis represented the LPGA Tour along with Lewis.
The play-off was necessary after the teams finished at 19 under at Rio Secco Golf Club in Henderson, Watney holing a 45-yard birdie putt on the final hole of regulation.
Watney and Kerr then parred the 18th to force a second extra hole, which Day claimed after a five-foot putt for birdie.
The Champions Tour team of Bernhard Langer, Fred Funk and Tom Lehman finished six strokes back.
"The women went 14 under on the back nine, but Nick holed a great, great putt to tie it," Day said. "Nick and I birdied the 18th and Davis birdied the 17th. Everybody won this as a team."
Love added: "Stacy started making a lot of birdies and Natalie had that chip-in on the 15th, and that got them going. They got hot on the back nine."
It was the ninth time the US PGA Tour won the event in its 21-year history.