The two leaders stand one stroke clear of Walter Hall, Doug Tewell and Bob Gilder, who opened with rounds of 5-under 67. Six golfers are tied for sixth place at minus-4, and defending champion Craig Stadler leads a group of 11 players knotted in 12th place one stroke further back.
Irwin and Quigley both played their rounds at Del Monte Golf Course, paired with one junior partner and two amateur players for a tournament hosted by The First Tee program.
Pebble Beach also hosted players -- all paired with a junior and two amateurs -- and will be the site of Sunday's final.
Irwin began his round on the back-nine and opened with consecutive birdies to reach minus-2. He made an 8-foot putt for his first birdie, and followed that with a 10-footer at the 11th.
After a par at No. 12, Irwin collected the third of his seven birdies at the par-5 13th when he set up a 6-foot putt with his pitching wedge to reach 3 under.
'I got off to a good start with birdies on three of four holes and kept it going the rest of the way,' said Irwin, a two-time winner on tour this year.
The 60-year-old Irwin stumbled to his only bogey of the round at the 16th, where he found a bunker and then missed an 8-foot par putt on the way to a five.
But Irwin made the turn at 3 under after a birdie at 18, and he made it two in a row when he two-putted from 30 feet at the par-5 first. Five straight pars followed until the 20-time PGA Tour winner closed with birdies on two of his final three holes to reach minus-6.
'Seven birdies and one bogey -- a good day,' said Irwin. 'I think 66 over here at Del Monte is a good round. It looks like [a course] you can tear up, but it's a test,' he added of the 6,357-yard track.
Quigley began his bogey-free round on the front-nine at Del Monte and opened with birdies on two of his first three holes. He strung together five straight pars after that and made the turn at 3 under after setting up birdie at No. 9 by knocking a sand wedge within 6 inches at the par-5 hole.
Also a two-time winner on tour this year, Quigley escaped a bunker at the 11th and made his 8-foot putt for another birdie. He carded two more birdies at Nos. 13 and 17 -- both par-5s -- to reach minus-6.
'I played really solid, no fives on the card' said the 58-year-old Quigley. 'I don't get too excited with first round scores, but you've got to be up there to have a chance. It's nice to be in the mix.'
The six golfers tied for sixth place are Curtis Strange, Mark McNulty, John Harris, Lanny Wadkins, Bruce Summerhays and Peter Jacobsen.