Still wearing a bandage on his finger after cutting it during the final round at Congressional Country Club, Stenson overcame some torrential afternoon downpours to grab an eagle and seven birdies.
Boyd, whose round included a 40 footer on the short 17th, said: "I holed some great putts when I needed to and that's been the difference the last couple of weeks.
"I've been working a lot on pace - the hole never comes to the ball, does it?
“Obviously the last hole was disappointing to finish with a six on a par five when I was in good position after my second shot. But I felt good on the golf course today and I'm looking forward to the next three rounds."
Compatriot Danny Willett, a team-mate of McIlroy at the 2007 Walker Cup, and Scotland's 1999 Open Champion Paul Lawrie had 66s to share third place with South African Jbe Kruger and Dutchman Tim Sluiter.
Twice US Open Champion Retief Goosen is two strokes further back and Sergio Garcia returned a 69, while on his 48th birthday - and on his return from commentating on McIlroy's amazing eight shot triumph - Colin Montgomerie managed a two under 70.
Alongside last year's Ryder Cup Captain are World Number Three Martin Kaymer, American star Dustin Johnson, defending champion David Horsey and 18 year old Italian Matteo Manassero.
Paul Casey would have been inside the top ten but for one hole, the 441 yard seventh.
Four under with three to play he hooked into thick rough, moved the ball only a few yards with his first two hacks at it, went over the fairway, then into a greenside bunker and eventually walked off with a quadruple-bogey eight, signing for a 72.