Parnevik closed with a 5-foot birdie putt on the par-4 ninth for a 5-under 66. Byrum finished 6 1/2 hours earlier, holing a 15-foot birdie putt on the par-5 18th at Pebble Beach for a 5-under 67.
Using a new putter and new putting style, Parnevik had six birdies and one bogey. The 50-year-old Swede is winless in 12 starts on the 50-and-over tour after winning five times on the PGA Tour.
The 54-year-old Byrum had five birdies in a bogey-free round. He was second last year, a stroke behind John Cook, and is winless in 62 career senior starts. Byrum won the 1989 Kemper Open for his lone PGA Tour title.
Mark McNulty was third at 4 under after a 68 at Pebble Beach, the site of the final round. He bogeyed the final hole.
Jeff Maggert opened with a 74 at Poppy Hills. He leads the tour with four victories - winning three of his last six starts - and tops the Charles Schwab Cup standings.
Cook had a 72 at Poppy Hills.