The duo stands at 9-under-par 135 for a two-stroke lead over Don Pooley (67), Lonnie Nielsen (67), defending champion Craig Stadler (68) and Morris Hatalsky (68).
Mark McCumber (69), Keith Fergus (68) and Walter Hall (71) share seventh place at minus-6. Dana Quigley, who shared the overnight lead with Irwin, shot a 73 and heads a group tied for 10th place one stroke further back.
Morgan played his round at Del Monte Golf Course, while Irwin competed at Pebble Beach, which will host the final round on Sunday. All players were grouped with a junior and two amateurs for the tournament, which is hosted by The First Tee program.
Morgan, who has six top-5 finishes this year without a victory, was in the clubhouse with the lead after a round that included seven birdies, one eagle and two bogeys.
The 23-time Champions Tour winner began the day on the back nine tied for 23rd place at minus-2 and made the turn at 6 under after five birdies and a bogey.
Morgan then reached minus-9 with an eagle at the par-5 first -- he holed out with a sand wedge -- and a birdie at No. 2.
'I thought I had a real chance at a low score after eagle-birdie, but I never did quite get it close enough after that,' said Morgan, who rolled in a 35- foot birdie putt at the par-3 sixth to briefly reach minus-10 before handing that stroke back with his second bogey of the day at No. 7.
Morgan's 65 was still the best round of the day.
'I started fast and played well all the way around, except for the last three holes,' said Morgan, whose best finish this year is a tie for second place at the Bayer Advantage Classic in June.
'I've never played this course. It's shorter than we normally play,' added the 58-year-old of the 6,357-yard Del Monte track.
Irwin began his round on the first tee at Pebble Beach and strung together five straight pars until a 22-foot eagle putt at the sixth put him at minus-8.
The 60-year-old moved further into red numbers with a birdie at No. 8, but he gave that stroke back when a poor pitch at the ninth led to his first bogey of the day.
Irwin dropped another stroke at the par-3 12th after his tee shot found a bunker, but he managed to tie Morgan for the lead with birdies on his last two holes. The tour's all-time money leader closed his round with a 15-foot birdie putt at No. 18.
'Probably one of the best ball-striking days I've had this year,' said Irwin, who is a two-time winner in 2005. 'If I continue to strike the ball like I did and improve my putting, I think I'll be right in there.'