Overnight leaders Rahm and Palmer shot a three-under 69 to finish on 26 under.

Fleetwood and Garcia finished three shots back after a final-round 68.

The win was the 42-year-old Palmer's first on the PGA Tour in more than nine years, while Rahm now has three wins in three years.

The duo paired up because Jordan Spieth - who played with Palmer at the event last year - was not taking part, and Wesley Bryan - Rahm's partner in 2018 - is recovering from shoulder surgery.

"It's been incredible," Rahm said. "The way it happened - he started off playing great, I kind of struggled and then I came through in the middle, and then he finished it off - it was amazing.

"To win as a team, it's something you don't get to feel very often in golf. I hope it happens again."

South Korea's Lee Kyoung-hoon and American Matt Every finished tied for third on 21 under with American Brian Gay and Slovakia's Rory Sabbatini.