Allen Doyle, who shared the first-round lead with Irwin, Keith Fergus and Gil Morgan, posted a 4-under 68 and stands alone in second place at 9-under-par 135.
Morgan and Fergus carded rounds of 69 and share third place with MasterCard Championship winner Dana Quigley (68).
Irwin won this tournament four straight years from 2000-03, while the event was not played in 2004 as it shifted from a late-fall event to an early season event.
Irwin got his second round going by getting up-and-down for birdie at the par-5 third. The Champions Tour's all-time wins leader dropped in a birdie putt from 12 feet out at the par-4 seventh.
He came right back to convert a 14-footer for birdie at the eighth to move to minus-8 on the Palmer Course at Turtle Bay Resort.
The 59-year-old Irwin collected his fourth birdie of the day at the par-3 13th when he holed out from a greenside bunker. He came right back with a 6-foot birdie putt at the 14th to get to 10 under.
Irwin parred three straight holes before two-putting for birdie at the last.
'I putted better today, but didn't play as well tee to green,' Irwin said. 'I'm trying not to consider the possibility of winning tomorrow for the fifth straight time.
'I seemed to play a little better on the tougher holes today. I want to make it where the guys have to beat me in the final round. I don't want to back up.'
If Irwin holds on for his 41st Champions Tour win, it would mark the first time in PGA Tour or Champions Tour history that a player has won the same event five straight times. It would also be his 100th top-three finish on the elder circuit.
Doyle, the 1999 runner-up here, got off to a hot start with a birdie at the first. However, he faltered to a bogey at the par-4 fifth.
The 56-year-old drained a birdie at the ninth to get back to 6 under. Doyle then converted consecutive birdies from the par-4 11th. After four pars, he birdied the 17th to take hold of second place.
Don Pooley (67) and Larry Nelson (68) share sixth place at seven-under-par 137. Jerry Pate, Don Reese, Tom McKnight, Dick Mast and Wayne Levi are one stroke-further back at minus-six.
Jay Sigel, the 1998 champion, heads a group of 11 players at 5-under-par 139. Bruce Fleisher, who won in 1999 and is the last player to win this event before Irwin's dominant run, stands nine shots back at minus-2.