Taylor carded four straight birdies from the 13th to the 16th holes to put himself on top of the leaderboard, while Mickelson missed a birdie putt from five feet on the last that would have forced a play-off.
“It’s been a long time. I didn’t think it was going to happen,” said Taylor as he celebrated his first PGA Tour event since 2005. “I worked so hard. I kept getting knocked down, knocked down. I’m just at a loss for words.”
Sweden’s Jonas Blixt finished third after a three-under round of 69 with Freddie Jacobson and Hirshi Iwata sharing fourth place a shot further adrift.
Taylor went out in 34 but it was after the turn that he really upped his game.
He hit his approach to within three feet on the 13th and on the par-five 14th he hit to within 12 feet.
On the 15th his shot out of the rough struck the ball of Matt Jones and stopped just two foot short of the cup.
And then at 16th hole he sunk a 30-foot putt for a fourth straight birdie that saw him circle the green in delight.
He had two further opportunities for birdie on the closing two holes but did not take advantage.
Mickelson, though, did not make it easy for Taylor watching from the clubhouse as, trailing by two with two to play he made a 12-foot birdie on the 17th.
But he then missed from five feet on the final hole as the ball clipped the left edge of the cup and spun away.
Bernhard Langer recorded his first victory since the anchoring ban was introduced as he completed a wire-to-wire win in the Chubb Classic.
Having spreadeagled the field with opening roinds of 62 and 66 at TwinEagles in Florida, the 58-year-old closed with a one-over 73 for a three-stroke victory over Fred Couples.
It was Langer’s 26th PGA TOUR Champions title, sitting third on the list behind Hale Irwin (45) and Lee Trevino (29).
“Whenever you make a drastic change or a change of some sort, you never know,” said Langer, who used a long putter to record his latest win after trying out various models earlier in the week.
“I’m 58 now, so if you look at the statistics, a lot of guys don’t win when they’re near 60.
“But I still think I have some good golf left in me and I’m glad the way I putted this week was probably better than I putted many weeks last year when I was anchored.
“That gives me hope that I can probably pursue with this style and still do very, very well.”
Colin Montgomerie (70-71-72) finished in a share of 26th on level-par while Sandy Lyle was tied 53rd after he signed for three 73s.
National coach Ian Rae is hoping to see Scotland’s strong showing at Leopard Creek in the inaugural African Amateur Stroke-Play Championship replicated in the future on the European Tour.
Five players, including runner-up Jamie Savage, finished in the top 10 at the traditional venue for the Alfred Dunhill Championship after Jack McDonald, Grant Forrest and Connor Syme had joined forces to win a team event incorporated within the main tournament by eight shots.
“It was a great week for the boys with some fantastic golf at a wonderful venue,” said Rae. “It was great to see Jamie finishing second after a poor 2015, so it will hopefully be onwards and upwards for him from here.”
The effort came hot on the heels of Ewen Ferguson being in the mix in the South African Stroke-Play Championship before finishing fifth.
“So far the trip has worked out really well,” added Rae. “The players are getting the chance to compete on Tour-level courses and gain valuable experience against other countries, but also playing in the type of conditions they will face if they get on to the European Tour.”