Campbell, who held at least a share of the lead since round two, shot a 1- under 71 at the Classic Club and ended the tournament at 25-under-par 335 for a three-shot victory and a $900,000 check.
'I hit a lot of bad shots out there, but I hit a lot of good ones as well,' said Campbell, who finished tied for second at the Sony Open last week.
Verplank missed a 12-foot birdie putt at 18 with a chance to end alone in second place. He finished with a 1-over 73 to tie Parnevik, who fired a 5-under 67 to reach minus-22. John Huston (68) was alone in fourth place at 21 under.
Two-time champion Phil Mickelson (71) tied for fifth place at 19-under-par 341 in his first event of the new season. Former winner Mike Weir (70) and John Senden (73) joined Mickelson there.
While Campbell parred his first five holes Sunday, playing partner Verplank mixed a pair of birdies with a bogey to tie the leader at 24-under. Both players then bogeyed the par-3 sixth.
There was a two-shot swing at the par-4 eighth, and it benefited Campbell.
Verplank found the rough and then a sand trap on his first two shots. He hit the bunker shot fat, ended up more than 100 feet away from the cup and rolled his par putt 20 feet past the hole.
After Verplank made his bogey try, Campbell followed with a 12-foot birdie putt to get back to 24 under for a two-shot lead.
Campbell extended his advantage with an eagle at the par-5 ninth. After a 390-yard drive, he knocked his second shot on the green and rolled in the 30-foot putt to reach minus-26.
At that point Verplank and Senden, also playing in the final group, were both four shots behind heading to the back nine.
They would soon get closer.
Perhaps feeling the pressure, Campbell pulled a 3-wood at the par-4 10th and left himself with 200 yards to the green after driving into the right rough. From there, he knocked his second shot into a green-side hazard and took a drop on the way to a double bogey.
That knocked Campbell's lead back to two shots, and he found more trouble at the par-4 13th when he drove into the water. After taking his drop, Campbell found a fairway bunker 150 yards from the hole. But he was able to get up-and-down for a bogey after hitting maybe his best shot of the round to within 8 feet.
'I think that kind of saved my round a little bit, kept my momentum going,' Campbell acknowledged. 'That was a pretty good shot, I'll just leave it at that.'
At 23-under, Campbell was just one shot ahead of Verplank and Parnevik, but he restored his two-shot lead with a 19-foot birdie putt at the par-5 14th.
Campbell and Verplank both played it safe with irons off the tee at the reachable par-four 15th. Campbell knocked his second shot within seven feet to set up another birdie, but Verplank bogeyed the hole after coming up short on his approach.
With his lead back to four shots, the win was basically in hand for Campbell. Verplank made it interesting with a birdie at the par-4 16th, but Campbell parred out to hold on.
Campbell's 71 was a far cry from his best fifth-round score ever, a 65 at this event in 2002, but it was also much better than his worst, a 77 here in 2003.
'I didn't play my best, but I was able to suck it up and get the win,' said Campbell, who played the tournament's par fives at minus-18 to beat his previous best 90-hole score by a stroke.
Olin Browne and Jeff Maggert shot matching, even-par 72s to share eighth place at 17 under. Justin Rose (74) and Bernhard Langer (72) led a group of six players who tied for 10th place at minus-16. Lucas Glover was also there after tying for the best round of the day, a 6-under 66.