The Englishman moved to two up with a birdie at the 13th and completed victory when the Korean bogeyed the 17th.
Wilson said: "It is not a good draw getting KJ. It was always going to be tough. He is a solid player tee to green and you are certainly not going to get him riled or anything and beat him mentally."
Fiji's Vijay Singh advanced with a 2&1 win over Denmark's Soren Kjeldsen while Phil Mickelson, drawn in Singh's quarter, beat Angel Cabrera after 19 holes.
Westwood, in the Ben Hogan bracket of the draw alongside top seed Singh and Mickelson, Ernie Els, Luke Donald, Graeme McDowell and last year's beaten finalist Cink, had raced into a three-hole lead after seven before the Thai won his first hole at the 8th.
Westwood lost again at the 15th but regained his two-hole lead at the next before sealing victory with a half at the 17th.
"I did play well," he said. "I was five under par and could have been a little better than that but Prayad played well and hung in there all day and started to come back at me on the back nine.
"I hit a great shot into 16 which sort of closed the game out - an eight iron to 18 inches which put me two up with two to play and I managed to halve 17."
Also through, Miguel Angel Jimenez sealed a second-round date with Colombia's Camilo Villegas by completing a 2&1 win over South Africa's Rory Sabbatini.
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