Mickelson, the defending champion at The Masters, closed with a 3-under 69 to end at 8-under-par 208. Beem tied him there with a 68. Those two were joined in the playoff by former Masters champion Jose Maria Olazabal (69), Brandt Jobe (67) and Arjun Atwal, who closed with the best round of the tournament, an 8-under 64.
Torrential rain Thursday and Friday pushed the first round back to Saturday. Another delay during the first round caused the round to be finished Sunday and tournament officials to shorten the event to 54 holes. The second round was completed earlier Monday before the third and final was contested.
It was also the second straight Monday finish, marking the first time that has happened since the 1983 season when three straight events - Tournament Players Championship, Greater Greensboro Open and The Masters - finished on Monday.
In the extra session, Atwal fell out after the first extra hole, No. 18. He had finished more then two hours before Mickelson and Olazabal had. The delay hurt Atwal as he pulled his second shot into the water and later missed a par putt.
Jobe also found water with his second, but had a chance to remain in the playoff. However, his 15-foot par putt missed and he was out.
So it came down to the three major champions - Olazabal, Beem and Mickelson, all of whom missed makeable birdie putts on No. 18, but moved on to the second playoff hole with pars.
Mickelson and Beem, the 2002 PGA Championship winner, each two-putted for par on the next extra hole, No. 17. Olazabal, the 1994 and 1999 Masters champion, pitched his third to 2 feet and tapped it in for par.
It was back to No. 18 for the third extra hole. Olazabal lost his drive well right. He pitched down the fairway with his second. Mickelson and Beem both knocked their second shots onto the green.
Olazabal, who was looking to become the first sponsor invited player to win since Adam Scott at the 2003 Deutsche Bank Championship, spun his third shot off the green and into the water.
He went to the drop area to hit his fifth, but dumped another one in the drink. He walked off knowing Beem and Mickelson would not make seven, which was the best he could make at that point.
'When Rich missed his putt on 18, I had another shot and just didn't make it,' said Olazabal. 'I had a second chance and didn't take advantage of it.'
Beem's lengthy eagle try slid by the edge and he tapped in his birdie putt. Mickelson, who was 15 feet closer and on nearly the same line as Beem, saw his eagle putt skirt the right edge. After he kicked in his birdie putt, it was back to No. 17.
On the fourth extra hole, Mickelson bombed one down the fairway for his eighth straight fairway hit. Beem hooked his drive into the left fairway bunker and missed the green right with his second shot. Mickelson dropped his second 15 feet from the hole.
Beem pitched his inside 2 feet, but it was not good enough. He watched as Mickelson rolled home his birdie putt to win his 26th PGA Tour title.
'In the playoff, I hit four good drives and that's something I'll need to do next week,' said Mickelson, who earned $900,000 for the win. 'The swing started to really feel good on the back side and even shooting 4 under there, there were putts I didn't make. So I felt like I kind of gave the tournament away, but I was able to somehow hang in there and get lucky.'
Mickelson was all over the place in regulation. After a birdie at two, he double-bogeyed the fifth. He came right back with birdies at six and seven. Lefty struggled to bogeys at the eighth and ninth though.
Around the turn, Mickelson carded four birdies, including one on the 18th, to make it into the playoff.
Olazabal posted one birdie and one bogey on the front nine. He then birdied three of his first four holes on the back side to get to minus-8. The Spaniard carded another bogey and birdie on the way home.
Atwal was more than 20th on the alternate list this week, but got into the event after nine players withdrew due to the early weather problems. The India native was the first into the clubhouse at minus-8.
The 32-year-old began on the back nine and carded four birdies and one bogey. On the front nine, Atwal birdied five holes, including three of his last four, to post an 8-under 64, the lowest round of the week.
Jobe was next in at 8-under. He carded a bogey-free 67 that included a birdie on the par-5 18th.
Beem, a three-time winner on the PGA Tour, bogeyed the second, but bounced back with a birdie at three. After eight straight pars, he birdied the 12th. and later birdied three of his last four holes to end at minus-8.
Frank Lickliter had a chance at the playoff, but knocked his second shot into the water at 18. He two-putted for bogey from 40 feet and ended at 7-under-par 209. He was joined there by Arron Oberholser, Tag Ridings and Scott Dunlap.
Lucas Glover also had a shot to get into the playoff, but slipped up on the par-5 closing hole. He knocked his second shot way right into the grandstands. After a free drop, Glover left his third shot short in the greenside pond.
The 25-year-old Glover eventually walked away with a double bogey to finish at minus-6. He was joined in a tie for 10th by Dennis Paulson, Charles Warren, Jay Williamson and Hunter Haas.