The German, co-leader overnight with American playing partner Spieth, produced rock-solid golf to move briefly four strokes clear, then survived a double-bogey on 15 as he closed with a one-under-par 71 at the challenging TPC Sawgrass.
Kaymer, whose previous win on the U.S. circuit came with his playoff success at the 2010 PGA Championship, nervously parred the last three holes in gathering gloom to post a 13-under total of 275.
The 29-year-old from Dusseldorf lined up a par putt from just under four feet on the 18th green, stroked the ball into the cup and then looked heavenwards in relief before pumping his right fist in celebration.
"It's very special for me," Kaymer told Golf Channel. "It is always very difficult to come back after a little (weather) break.
"Obviously you see the leaderboard, you see where you are. The first 14 holes, I played really, really well. And then you are really disappointed when they called it (halted play).
"And then you are a little cold. I made a couple of wrong decisions on 15. But a big putt on 17."
Spieth, who at 20 was aiming to become the youngest champion at the prestigious PGA Tour event widely regarded as the unofficial fifth major, briefly led by a shot early in the final round before fading to a 74 and a tie for fourth at 10 under.
Level with Spieth was U.S. Open champion Justin Rose (69), whose two-stroke penalty imposed after the third round was rescinded earlier in the day following a review by the game's governing bodies and PGA Tour Commissioner Tim Finchem.
American Jim Furyk signed off with a flawless six-birdie 66 to secure outright second place at 12 under, one stroke better than Spaniard Sergio Garcia (70).
Kaymer and Spieth both made a fast start to the final round as they sank eight-foot birdie putts at the par-five second to move to 13 under, maintaining a three-shot cushion.
Spieth forged one ahead with a superb birdie at the fourth where he struck his approach to seven feet and buried the putt, but recorded his first bogey of the tournament at the tricky par-four fifth after finding the left rough off the tee.
The young American also bogeyed the par-three eighth, after his tee shot clipped some trees to the left of the hole, to hand the German a one-shot lead.
Kaymer, who had not won a tournament since the Nedbank Golf Challenge in South Africa at the end of 2012, then got up and down from a greenside bunker to birdie the par-five ninth and double his advantage.
Spieth dropped another shot after his approach at the par-four 10th bounced over the back left of the green to hand Kaymer a three-shot lead.
The German tightened his grip on the title by draining a 12-foot birdie putt at the par-five 11th to stretch his lead to four shots before Furyk trimmed that to three when he birdied the 16th.
Kaymer had good birdie opportunities at the 12th and 13th but ran both putts inches short of the cup before play was suspended for just over 90 minutes due to the threat of lightning with 11 players still out on the course.
Once play resumed in light drizzle, Kaymer made a complete mess of the par-four 15th where he double-bogeyed after pulling his drive left into trees, missing the green with his approach and hitting a poor third shot into a bunker.
That cut his lead to just one and he parred 16 before miraculously avoiding more trouble at the infamous 17th where his tee shot very nearly spun back into water.
He then chipped 28 feet short of the hole and stunningly drained the par putt.
After splitting the fairway off the tee at the par-four last, Kaymer ended up short of the green with his approach before he two-putted from there to clinch the title and the winner's check for $1.8 million.
Adam Scott fell well short in his bid to become world number one for the first time this week, closing with a 73 that included three bogeys and two birdies.
When the Australian signed his card, he was in a tie for 39th, having needed to finish no worse than joint 16th to have a chance of dislodging the absent Tiger Woods from the top spot.
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