Beckman produced a seven-under par round of 63, with five birdies on the back nine, in Scottsdale, Arizona to finish level with overnight leader Sutherland on 18-under par.
After the pair made par on the first play-off hole, the 18th, Sutherland drove his second shot on the second play-off hole into desert rough and then went down a hill behind the green while Beckman kept his nerve to par and claim victory, which secured his tour card for the next two years.
The victory was Beckman's second on the PGA Tour, following his win in Mississippi in 2001.
"I'm a little surprised. I mean, I've had such a poor year, and I had back problems. I had to skip eight weeks, and its just been a tough year," said Beckman.
"I honestly was thinking about quitting he game, that's how bad I felt.
"I can't explain to you how good I feel right now. I don't know what it was and why I did it but I just felt good all day and it happened for me."
Sutherland had his chances, missing a birdie on the 18th and then failing to take a tough putt on the first play-off hole.
"I had a couple putts to win that - the one in regulation, I hit it on-line, I just didn't hit it hard enough and then I pulled the one in the playoff," he said.
Sutherland was left to rue the decisive second shot on the second play-off hole when he shot the ball wide to the right and into dirt close to a tree that limited his movement.
"I got in the fairway, and my ball was in a ball mark," said Sutherland. "It was like a quarter plugged.
"The ball really squirted right. I made pretty good contact on it but it was right all the way. It wasn't the lie I was looking for but that's the way it goes."
Australia's Mathew Goggin finished one stroke behind the leading pair after firing an excellent seven-under par 63.
Last year's winner, Canada's Mike Weir, the top-ranked player in the event, made a late charge with a final-round 63 but was still four strokes behind Beckman and Sutherland.
Australia's Steve Allan, among the frontrunners all week, finished tied for seventh after three-putting for a bogey on the 17th and then finding water and making a double bogey on 18.