The Victorian shot a 7-under 64 to share the lead with Richard Bland, the two opening up a two-stroke lead over the field on Thursday.
Green played in the morning and posted three birdies and an eagle on the par 5s.
He was off to a quick start when he hit a hybrid from about 250 yards on the par-5 fifth hole to set up eagle.
"Hit it just perfect and just shaped it in there nicely and it was tracking towards the hole," Green said.
"I think it ran across the edge of the hole and finished about maybe 7 feet past the hole. So that was obviously one of those exceptional holes at the right time to get the round going really well."
He added birdies on three more par 5s to offset his lone bogey at No.6.
Bland, taking a break from his LIV Golf schedule to make his senior major championship debut, had a chance to pass Green late in the afternoon until he had to scramble for par on No 8 after a rare bad tee shot, and failed to birdie the par-5 ninth.
Bland has the game for Harbour Shores, mainly for his accuracy off the tee, and that helped to keep bogeys off his card. He didn't miss a fairway until his 17th hole, the par-4 eighth.
"I drove the ball really well, which is a strength of mine, which you need around here," he said.
Their closest rivals include a group comprising defending champion Steve Stricker.
Stricker had never seen Harbour Shores until this week and felt uncomfortable with some of the sight lines off the tee. He still managed seven birdies, his round slowed by a double bogey on the par-4 16th when he pulled his tee shot into a hazard.
"We've got a long way to go, but it was important to get off to a good start," he said. "I'm surprised the scores are that low."
Mike Weir, K.J. Choi, Scott Dunlap and club pro Jeffrey Schmid joined Stricker at 5-under 66. Two-time PGA champion Vijay Singh, who chose not to play at Valhalla last week, and Stewart Cink were among those at 67.
Australians Scott Hend and Mark Hensby are in contention after opening with 3-under 68s.
They are tied 13th, one shot better than compatriots Cameron Percy and Greg Chalmers.
Bernhard Langer, riding in a cart as he tries to fully recover from a torn Achilles tendon in February, opened with a 74.
He was at 1 under for his round until a double bogey-bogey-bogey finish. Langer said he hopes to be back to walking 18 holes in a few more months.
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