Karlsson, who had led by as many as six strokes, carded back-to-back bogeys on the final two holes, concluding the day with a 2-under 68 and ending three rounds at 11-under 199.
That was still one stroke better than Harrison Frazar, who birdied the 18th hole en route to a round of 6-under 64.
Karlsson has 11 European Tour titles but none on the PGA Tour. This is his first season playing full time in the United States.
The Swede lost in Memphis last year in a playoff to Lee Westwood.
Alone in third at minus-8 was John Merrick, who posted a 3-under 67.
Retief Goosen claimed fourth after firing a 6-under 64.