With an 18-under total of 192, Parnevik had a three-shot lead over countryman Mathias Grönberg.
Parnevik has torn through LaCantera Golf Course this week with just four bogeys in three rounds.
On Thursday, he shrugged off a bogey at his first hole to card 10 birdies in a career-best nine-under 61.
He followed that with a 65 on Friday and had six more birdies on Saturday to set himself up for his first USPGA Tour victory since the 2001 Honda Classic.
Parnevik had an uneven start to his round, birdying his first hole but following it with a bogey.
He added a birdie at seven, and started his back nine with a bogey at 10 before a strong finish.
“It was a little bit tougher than I expected out there. The wind was blowing a lot more, but I was a little bit more uptight, even though I got off to a great start,” Parnevik said. “Hit a wedge to about four feet on one and holed the putt, but I missed a short one on the second hole which tightened up my putting stroke quite a bit and felt pretty average over the putts after that.”
Three straight birdies from the 11th put Parnevik back in control. He added his last birdie at 17.
“I hung in there. I did a terrible bogey on 10. I thought I hit a good driver, had a wedge in there, made bogey,” Parnevik said. “I figured it ticked me off a little bit because I birdied the next three. That was a good thing.
For not having a great day, I’m very happy to shoot four-under-par.”
Grönberg fired six birdies with one bogey in a 65 that kept him in second place at 15-under 195. He had two birdies on the front nine and after a bogey at 10, Grönberg had consecutive birdies at 12 and 13 and again at 15 and 16.
“I obviously had a hiccup. I three-putted from off the fringe on 10,” Grönberg said. “I had actually holed the putt on two and three off the greens so I felt really good about making the putt and hit it slightly too hard and got maybe a three-footer coming back and I missed it, pulled it a little bit.
“I played pretty good on the front nine except I hit a couple of shots that I didn’t like with my irons today, little bit thin and not really greatly struck.
“But, except for that, I was very, very proud and pleased with and maybe because I was kind of patient that I managed to get it back to five-under today.”
Justin Leonard, who won this event in 2000 and 2001, was in third at 14-under 196 after a bogey-free 64.