“It’s probably the most emotion I have ever shown in a happy way,” said Lawrence, who hit eight birdies in a bogey-free round to set the clubhouse lead on 18 under.
“I fought so hard and just gave it my everything. I feel for Paul, he played great golf and it looked like it was his all day, even in the play-off. He missed a couple of short ones, but it’s just the best feeling in the world.”
Casey started the day six shots ahead of Lawrence, but struggled to rekindle the form that saw him hit 64 and 63 in his second and third rounds.
The LIV golfer dropped shots on three of his opening eight holes, including a double bogey six on the sixth.
Casey was two over for the day after a bogey on the eighth, but then picked up five birdies in the next seven holes to reclaim the lead.
The world number 707 made it up and down from a greenside bunker to save par on the 16th, then narrowly missed another birdie putt on the 17th to leave himself needing a par on the last for victory.
But he was unable to navigate the par four 18th safely after finding thick rough from the tee. Casey bounced his approach off a rock and over a stream into the rough guarding the green and after a poor chip shot missed a 20-foot putt for victory.
The difficult 18th hole was chosen for the play-off.
Both golfers made pars in their first two attempts, with Casey missing a 10-foot birdie putt to win on the second play-off hole.
Tournament organisers changed the pin position for the third play-off hole in an attempt to separate the two, but again they both made pars, with Casey seeing his eight-foot putt for the championship hit the cup and roll out.
And Lawrence finally punished his opponent on the fourth play-off hole.
