Mickelson carded a five-under par 65 Sunday for a nine-under winning total of 271, his first victory since his wife and his mother were diagnosed with breast cancer this year.
Woods, who missed the playoff series last year as he recovered from knee surgery, captured the prize for the second time in three years.
Woods closed with a 70 that put him second behind Mickelson on 274, and his runner-up finish was enough to deliver the FedEx Cup title after he came into the tournament atop the points standings.
The FedEx title rewarded a year that included six tournament victories for Woods.
Woods didn't make a birdie until the 15th hole as his streak of eight straight rounds in the 60s came to an end.
Mickelson, who regained the world number two ranking with the victory, earned a three million-dollar FedEx Cup bonus - in addition to his 1.35 million-dollar tournament winner's prize - as the second-placed finisher in the points.
He started the tournament 14th in the standings, and would have needed Woods to finish eighth or worse to have any chance of seizing the top playoff prize.
A handful of players were in the hunt for the FedEx Cup over Sunday's back nine.
Overnight tournament leader Kenny Perry had a shot at the Cup until a bogey at the par-five ninth signalled the start of an unravelling that left him with a 74.
With Mickelson winning the tournament, Steve Stricker had only to finish in front of Woods to claim the 10 million-dollar series bonus. Stricker looked capable of doing just that, until a muddy ball in the 16th fairway cost him a bogey. He closed with a 69 that left him in sixth.
Mickelson, still benefitting from putting tips from former PGA Champion Dave Stockton, made consecutive birdie putts of 15 feet on the third and 30 feet at four.
He seized a share of the lead at eight, where his approach left him a tap-in for birdie. He played the final 20 holes of the tournament without a bogey.
Woods, in contrast, didn't get a one-putt birdie on Sunday until he draind a 35-footer at 16.
"Phil played well. He did the things he needed to do this week," Woods said. "Unfortunately, I didn't putt well and consequently, I didn't push him. Phil ran off and got away from us."
Mickelson quipped that it just didn't seem right that runner-up Woods was walking away with a 10 million-dollar prize.
"Let me see if I get this straight," Mickelson said. "I shot 65 and he shot (70), and he gets a check for 10 million?
"I'm just kidding," Mickelson added. "I didn't play well in the first three (playoff) events to give myself a chance."