Maggert, whose lone PGA title came at the 1993 Disney Classic, holed a seven-iron from 185 yards for an eagle on the par-four sixth hole and added five birdies to offset a pair of bogeys.
Long-driving John Daly and fellow American Stewart Cink were one stroke off the pace. Scotland's Colin Montgomerie and the former winner Steve Pate are another stroke back at 69.
Montgomerie, still seeking his first win on the US PGA tour, had birdies at two of the final three holes.
Daly, trying for his first win since his latest bout with alcoholism, started on the 10th hole and tore up the back nine with four birdies. But he played the front side at even par and settled for second.
"This is the best I've felt about my game ever," said Daly, whose four career victories including triumphs at the 1991 PGA Championship and 1995 British Open. In addition to alcohol problems, he still fights food cravings.
It was the 17th time in his last 18 rounds that Daly has shot par or better, a streak that has earned him a tie for fourth in Los Angeles and three other finishes in the top 20. He has won $204,850 (pounds 125,000)in six starts, nearly twice as much as he won last year when he missed two months after another stint in alcohol rehabilitation.
"I've been hitting it very well," he said. "I practice and am doing the right things each day. The cravings for food have been tough, so I'm not going to worry about my weight."
Sixteen others are three behind Maggert, including the defending champion, Stuart Appleby of Australia, the 1987 champion, Mark Calcavecchia, Vijay Singh of Fiji, Bernhard Langer of Germany and the US veteran Tom Watson, runner-up in his two prior 1998 events.
Singh appears set to extend the PGA's longest current streak of consecutive cuts made to 51.
Maggert gained momentum with a short birdie putt at the seventh and a 35-foot birdie on the ninth, then finished with birdies on two par-five holes, the 14th and 16th, sinking a 10-footer on the latter. "I have been playing pretty well," Maggert said. "It does bug me that I've only won once. Sooner or later I'll get over the hump."Reuse content