Irwin, who is trying to win this event for the fifth time in his career, joined R.W. Eaks, Dave Barr and Tom McKnight in a tie for second place at 3-under-par 69.
The Australian recovered with a birdie at the par-3 17th and reached the green in two at the par-5 18th. Marsh two-putted for birdie and kept on rolling at the par-4 first after his second shot stopped within 14 feet of the hole for another birdie.
Marsh, a two-time major winner on the Champions Tour, hit an 8-iron to 6 feet at the par-4 second and rolled in the putt for another birdie. Marsh then took the outright lead at the par-3 eighth after his tee shot landed within 18 feet of the hole. Marsh drained the birdie try to secure the first-round lead.
'It's a long golf course,' Marsh said. 'But obviously I'm very happy to be where I am. On a golf course like this, driving the ball in the fairway, is of paramount importance. And I did that for the most part today.'
Marsh has only one top-10 finish in seven events on the Champions Tour in 2005, and the 61-year-old has finished well out of contention in his last two starts.
'I had two pretty miserable weeks,' said Marsh, a six-time winner on the Champions Tour. 'But I made a few changes to my putting this week and got back in an old putting style that I have done well with in the past.'
The early part of 2005 has been more of the same for Irwin, who already has two wins to his name. Irwin, the all-time wins leader in Champions Tour history, got off to a good start at the season's first major with a birdie at the par-4 second.
The 59-year-old struggled with a bogey at the following hole, however, and found trouble again with a bogey at the fifth. Irwin recovered with a birdie at the seventh to make the turn at even-par.
The three-time U.S. Open winner made a move down the stretch and played his second shot inside 3 feet for a birdie at the 15th. Irwin then birdied the 16th and converted a 10-foot birdie putt at the last to finish within one of Marsh.
'The score indicates a much better round than what I played,' said Irwin. 'I really didn't hit the ball that well. So I don't want to get terribly excited because sometimes in this game just when you think you got it, it's got you. I'm happy with the score, but certainly I need some work to make it look a little better.'
Eaks started on the back nine and struggled early with a pair of bogeys over his first six holes. Eaks countered with an eagle at the par-5 18th and tallied four birdies early on the front nine to surge into the lead.
The 53-year-old stumbled coming in with a bogey at the ninth for his share of second.
McKnight birdied three of his last six holes to finish one shot off the lead while Barr mixed six birdies with three bogeys for his 69.
'Right now I'm just kind of going day by day and just hoping that I can stay together,' said Barr, who suffered through the practice rounds because of a pulled back muscle. 'Hopefully things well be a little bit more looser tomorrow and we'll just go out and see what happens.'
Curtis Strange had a hot start with three birdies over his first four holes. Strange, who hasn't won since his second consecutive U.S. Open title in 1989, cooled off on the inward half with a bogey at the 11th and back-to-back bogeys from the 16th.
The Champions Tour rookie responded at the par-5 closing hole and just got his second shot over the water protecting the green. Strange's ball rolled 8 feet of the hole and he ran home the eagle try to finish within two of Marsh after a round of 70.
'They had the tees up today to make us all go for it. I like that,' said Strange. 'And I got fortunate and hit it near the hole and made the putt.'
Strange was joined by Ray Floyd, Bob Gilder, Perry Arthur, Jerry Pate, Hajime Meshiai and Mike Reid in a tie for sixth.
Tom Watson was one shot further back at 1-under-par 71 along with Peter Jacobsen, Tom Kite, Gil Morgan, Dana Quigley, Bruce Fleisher, Don Reese, Jon Chillas and Luis Carbonetti.