Jay Haas, who won this event in 1988, finished tied for second alongside Canada's Mike Weir at 25-under-par 263.
Herron is making only his second appearance at the Hope. While he usually passes on the tournament, the 2003 edition has been particularly kind to the former University of New Mexico star.
'You know, I've made a lot of decisions that backfired,' said Herron, who also tied the PGA Tour record for most strokes under par after 72 holes. 'I knew I've been putting well and driving it pretty well. I just knew that this would be a good tournament. When I saw the schedule, it fit perfectly in my schedule and decided to come play a Pro-Am.'
Herron played Indian Wells on Saturday and struggled early on with a bogey at the par-4 first. He settled down with three straight pars before a 10-foot birdie at the fifth sparked a run.
The 32-year-old hit his tee shot to 15 feet for birdie at the par-3 sixth and dropped a sand-wedge inside two feet for a birdie at the seventh. Herron then reached the green in two at the par-5 eighth and two-putted for his fourth consecutive birdie.
Herron hit a 7-iron to 15 feet for a birdie at the 10th and added back-to- back birdies starting at the par-3 13th to reach 28-under.
At the par-4 16th, Herron sent his drive in the left rough and hit his approach to the front of the green, 40 feet from the cup. He ran the putt home for birdie and nearly added to his advantage on the final two holes.
Herron's birdie try at 17 lipped out and he failed to convert at the last. Nonetheless, he built a favorable advantage heading into the final round of this marathon event.
'I enjoyed the day,' said Herron, who is looking for his first victory on tour since the 1999 Bay Hill Invitational. 'I've got to shoot low tomorrow. It's kind of the moral of the story in this tournament.
'All I can do is try to look positive. This game will beat you down very quickly, and you've just got to somehow stay positive.'
Weir had a disappointing season in 2002 without a single top-10 finish. He made his 2003 debut with a top-10 in Phoenix last week and has put himself in contention here after a fourth-round 67 at La Quinta.
'Obviously, I was not happy about my year last year. I think I needed time away from the game more than anything,' said Weir. 'I haven't done anything special. I just needed a little break from the game to refresh my mind, really, more than anything, to be really prepared to get out here and play golf.'
Chris DiMarco had seven birdies and one bogey for a round of 66. He finished tied for fourth alongside David Gossett at 24-under-par 264.
Stephen Ames, who held a share of the third-round lead, carded a 71 to finish one shot further back along with Chad Campbell at 23-under-par 265.
John Maginnes, Kenny Perry, Doug Barron, Steve Lowery and Pat Perez finished tied for eighth at 22-under-par 266.
Defending champion Phil Mickelson collected six birdies and three bogeys for a round of 69. He finished in a group at 18-under-par 270.
The 72-hole cut fell at 13-under-par 275 with 72 players making it through to the final round on the Palmer Course at PGA West.
Among those who did not qualify were David Duval, who was playing in his first event of the season, and reigning PGA Champion Rich Beem.