It was Rahm's second PGA Tour title and fourth worldwide victory in a year and the win will see the 23-year-old Spaniard jump from third to second behind Dustin Johnson in the world rankings.
"It's, again, I said it many times, I never thought I was going to be at this point in my life right now, especially the way I won both victories, it couldn't be anymore different than the other".
Rahm overcame surprising par-5 problems in regulation to shoot 5-under 67.
"To follow-up a shot that ended up one foot away, had a makeable birdie putt every time, it's awesome that he kept up and one of us had to do it and either one of us would have been a well-deserving champion". They finished at 22-under 266.
"Tournaments like this build character".
"I hit a lot of really good putts today that didn't go in", he said.
After Rahm made his birdie putt on the fourth playoff hole, Landry missed an 11-footer. "I saw the break, I knew it was outside the left edge, I just trusted myself, trusted my stroke and hit a flawless - actually a little bit below ideal speed and caught the lip and went in".
Fellow former Arkansas player Andrew Landry and Martin Piller were a stroke back, and Jon Rahm and Scott Piercy were 17 under. Rahm shot a five-under 67 Sunday to get into the play-off. Fleetwood birdied six of the final nine holes to overtake Ross Fisher. The Dallas native and resident squared three bogeys at holes 6, 9 and 10, outpaced by five circles at 2, 7, 8, 11 and 14, all from inside of 12 feet. Garcia returned to the course just after dawn to complete his third round after play was suspended on Saturday because of lightning strikes.
Cook, who captured his first tour title in November at the RSM Classic at Sea Island, Georgia, fired seven birdies and an eagle and rolled in a tough par-saving putt at the 18th at La Quinta Country Club, one of three courses in use over the first three rounds of the tournament. It was the third win on the over-50 tour for the 51-year-old Kelly. Montgomerie shot 69. David Toms shot 67 and finished two shots back, and Miguel Angel Jimenez was another stroke behind after a 66.