McIlroy looked free and easy and saw only opportunity at Southern Hills, blasting his driver over trees and into fairways, setting up some of his seven birdies that carried him to a five-under 65 and an early one-shot lead.
Woods picked his spots and was never terribly crisp on a right leg he said felt worse than it did at the Masters last month. He fell apart in the middle of his round and at the end, finishing with two bogeys for a 74 and his worst start to a PGA since 2015.
It was just what McIlroy needed as he tries to end nearly eight years without a major, many of those chances doomed by bad starts.
This was his lowest start to par since a 5-under 66 when he won the PGA at Valhalla in 2014, the most recent of his four majors.
"I think when your game is feeling like that, it's just a matter of going out there and really sticking to your game plan, executing as well as you possibly can and just sort of staying in your own little world," McIlroy said.
"I feel like this course, it lets you be pretty aggressive off the tee if you want to be, so I hit quite a lot of drivers out there and took advantage of my length and finished that off with some nice iron play and some nice putting."
Will Zalatoris and Pebble Beach winner Tom Hoge each opened with 66 to be one behind, while Matt Kuchar and Abraham Ancer were another shot behind.
McIlroy and Woods were joined in the group by Jordan Spieth, who lacks only this major to complete the career grand slam and arrived in Tulsa with his game in good form. But a series of missed birdie chances was followed by a series of missed par putts, and Spieth never quite recovered. He had a late birdie and saved par on his final hole at No.9 for a 72.
Four straight birdies for McIlroy shot the Northern Irishman clear early and he never relinquished the lead before signing off with another birdie on his final hole of the day.
Only 17 of the 78 players from the morning wave broke par.
Australian Cameron Smith was on, the world No.4 in a tie for sixth at two under after collecting seven birdies.
In one other key part of Southern Hills' history, five of the seven champions at the course have at least had a share of the 18-hole lead.