The 5-foot putt on the 18th hole of the TPC Southwind course gave Westwood his second PGA Tour victory.
Westwood (2-under-par 68), Karlsson (69) and third-round leader Robert Garrigus (71) began a three-way playoff after each finished 72 holes at 10-under 270.
Garrigus blew a three-stroke lead on the final regulation hole in an epic collapse to force the playoff. He missed a long double-bogey putt that would have left him hanging onto a one-stroke lead and the tournament victory.
Garrigus dropped out of the playoff after the third hole, leaving Westwood and Karlsson to compete in a sudden-death showdown.
On the final hole, Karlsson missed a birdie putt to open the door for Westwood.
Shaun Micheel and Garrett Willis each carded 3-under 67s Sunday to end tied for fourth place at 9-under 271.