US Ryder Cup star Kim needed a first play-off hole success over Taylor to claim the third PGA Tour victory of his career.
Kim, 24, had held a three-shot lead over the field heading into the back nine of his final round at Redstone Golf Club having started the day in a share of the 54-hole lead with fellow American Bryce Molder at 10 under par.
He was still on course for victory at the 72nd hole when he missed a five-foot putt to bogey for a two-under-par 70 and allow the watching Taylor, who shot a 68, to join him in a sudden-death play-off.
Kim's wobbles were over though as he played the tricky par-four 18th to perfection while Taylor emulated his rival's play at the 72nd when he found successive rightside bunkers in his bid to avoid the left-sided lake.
Kim two-putted from 30 feet for par as Taylor failed to hole out and victory was secured.
South African Charl Schwartzel fired a closing 67 to leapfrog into a tie for third place at 11 under with Canada's Graham DeLaet (68), a shot behind Kim and Taylor, while 2003 US PGA champion Shaun Micheel claimed fifth place thanks to a final-round 65.
England's Westwood rallied over his closing holes to engineer a tie for eighth heading into next week's Masters.
The European number one and world number four had followed rounds of 69 and 68 with a level-par 72 on Saturday, and he undid a birdie at the first with back-to-back bogeys at the third and fourth holes.
Birdies at the 12th, 14th and 15th got him to nine under and in spite of a bogey at the 16th Westwood hung on for his second Stateside top-10 of the year following a tie for ninth at the Honda Classic.
Justin Rose was the next best European following his third round of 70 this week, leaving the Englishman at six under for the tournament and in a tie for 14th with Sweden's Fredrik Jacobson closing at five under after a 71.
Denmark's Soren Kjeldsen was at three under after a final round of 69 but Ireland's Padraig Harrington could not have enjoyed his Sunday at Redstone.
The three-time major winner shot a five-over 77, a final round that included two double bogeys, four bogeys and three birdies.
That left the Dubliner at one under for the week, where Scotland's Martin Laird finished his week thanks to a closing 71.
