They played No. 18 again in the playoff and Kim made a routine 4, two-putting from 30 feet. Taylor hit a bad drive, played out of the greenside bunker and came up short on his 18-foot par putt.
The 24-year-old Kim won for the first time since the 2008 AT&T National. He also won the Wachovia Championship in 2008.
The Houston Open went to a playoff for the second straight year. Paul Casey beat J.B. Holmes last year with a bogey on the first extra hole after Holmes drove into the water.
Charl Schwartzel (67) and Graham DeLaet (68) finished one stroke back at 11 under. Shaun Micheel (65) was two shots behind and Kevin Stadler (68) and Houston resident Jeff Maggert (70) finished four behind.
Taylor played in the group ahead of Kim and rolled in an 18-foot birdie putt on the 18th hole. He backpedaled as the ball curved toward the hole and flipped his putter in the air when it dropped.
Kim, who shared the third-round lead with Bryce Molder, birdied the first hole on Sunday and maintained the outright lead until the bad putt on 18. He hit his approach into the greenside bunker, blasted out to six feet and missed to the right.
He struggled with his tee shots all weekend, but found the fairway on the playoff hole. Taylor hit the bunker on the right off the tee and couldn't recover, missing a chance to qualify for next week's Masters in his hometown of Augusta, Ga.
"Hugely disappointed," Taylor said. "It's a tough pill to swallow."
Kim hit only 23 of 56 fairways in four rounds, the fourth-lowest total for a winner since 1983. He still earned his fourth straight top-25 finish this year and broke 70 for the fourth straight final round.
His last birdie on Sunday came at the short, par-4 12th, when he drove into the greenside bunker and got up and down for another birdie.
Taylor made the turn at 10 under, then birdied Nos. 12 and 13 to get a stroke away. Kim saved par with a delicate pitch from behind the 14th green, one of six straight pars before the short miss on 18.
He pulled out the victory on the extra hole, though, becoming the fifth player currently under 30 with three or more PGA Tour victories.
Earlier in the day, Phil Mickelson finished 2 under after an eventful 71. He double-bogeyed three of his first 10 holes, then reeled off six straight birdies to match the best streak on tour this year. Matt Every birdied six consecutive holes in Phoenix.
During his hot stretch on the back nine, Mickelson pulled a special guest out of the gallery to carry his bag. Dr. Tom Buchholz, a radiation oncologist at the M.D. Anderson Cancer Center in Houston, is treating Mickelson's wife and mother, Amy and Mary, who were both diagnosed with breast cancer last summer.
Buchholz wasn't totally inexperienced. He was working in the pro shop at the Westchester Country Club after college in 1984 when he caddied for Allen Miller in the PGA's Westchester Classic. Miller tied for 10th.
"It was a story we talked about over the many hours and weeks and months we've been together in the hospital," Mickelson said. "We went 3-for-3, three birdies."
Light rain fell in the morning, but the tournament avoided a weather delay for the first time since 2005.