Pettersen and Matthew tied at 11-under-par 205 through 54 holes and headed to the par-5 18th hole for the playoff. Both posted pars the first two extra holes but Pettersen made a birdie putt on the third playoff hole while Matthew settled for par.
It was the ninth LPGA title for Pettersen but first since August 2011. Her first five titles, including a win at this event, all came in 2007.
Pettersen started the final round with a five-stroke lead with Ryu So-yeon in second, struggled Sunday to a 2-over 74. Ryu, who shot 73 Sunday, however, was passed by several players. That group included Matthew, who was 6-under through 14 holes, which put her in front by two. She had a bogey at the 16th that left her at 11-under for the tournament.
Pettersen had double bogeys at Nos. 3 and 12 and a bogey at the eighth hole -- all par 3s. She had birdies at 4 and 10 and another birdie at 14 allowed her to take a spot in the playoff.
Yani Tseng fired a 3-under 69 Sunday and finished third at 10-under and Pak Se-ri was fourth at 9-under 207.