Jerry Pate had five consecutive birdies on the back nine en route to a round of 68. He was joined by Jim Thorpe, Wayne Levi, Ron Streck and Leonard Thompson in a tie for fourth.
McCullough, a two-time winner on the Champions Tour, jumped out of the gate with a birdie at the first at The Club at TwinEagles. He then birdied the par-4 fourth and cruised with five straight pars to make the turn at 2 under.
The 59-year-old picked up steam on the inward half with back-to-back birdies starting at the par-4 10th. McCullough then birdied the par-5 13th and added a birdie at the par-4 15th on his way to the first-round lead.
Eaks ran off four birdies over his first nine holes and a birdie at the 10th lifted him to 5 under. He stumbled from that point on, however, with a bogey at the 12th and another dropped shot at the 14th.
The 52-year-old responded down the stretch and birdied each of his last three holes to join McCullough in the lead.
Irwin, who has continued his winning ways in 2005 with yet another victory at the Turtle Bay Championship, drained a 20-foot putt for a quick birdie at the first and picked up a birdie at the par-5 third.
'I wanted to get off to a good, solid start,' said Irwin, who won this event in 1997 and 2002. 'Got a little loose with some putting in the middle, but overall I did lots of things well today.'
He played a wedge inside 12 feet for a birdie at the par-4 10th and dropped his approach within 15 feet of the hole for a birdie at the par-4 14th.
Irwin sent his tee shot into a bunker at the par-3 16th and hit out of the sand to 10 feet. He calmly sank the par putt and landed his third shot 6 feet from the hole for a birdie at the par-5 17th to finish within one of McCullough and Eaks after a round of 67.
'I'm still fighting a cold I've had for a few days,' he said. 'I'm glad to get through today and now I'll recharge and get ready for tomorrow. You can't afford that casual round out here.'
Defending champion Craig Stadler managed a round of 73 on Friday to finish in a tie for 46th at 1 over par.
Two-time U.S. Open champion Curtis Strange was one shot further back at 2-over-par 74 in his Champions Tour debut.
'I hit some good shots,' said Strange. 'I was actually pretty enthusiastic about playing today. It's just what happens. I'm aggravated, but I knew it was going to be like this. It's competition. Everything's on the line.'
Strange bogeyed his opening hole, but countered with a birdie at the par-3 second. The 50-year-old found trouble with bogeys at the seventh and ninth before he knocked his second shot inside 3 feet for a birdie at the par-4 10th.
He suffered a double-bogey at the 12th, but was able to recover again with back-to-back birdies from the 13th.
At the closing hole, Strange drove into a fairway bunker and took a shot at the green only to see his ball fall just short in the water guarding the putting surface. He took a drop and walked away with a bogey, but there is plenty of golf left before the former Ryder Cup captain's first week on the Champions Tour is through.