Woods has played on only one victorious Ryder Cup team (1999) in seven appearances, an astonishing number for one of the game’s all-time greats.
Kirk, 2014 winner of the tournament, birdied four of his first seven holes to shoot four-under 67 at TPC Boston in the second round of the FedEx Cup playoffs.
Spieth shot a superb six-under-par 65 in benign conditions on Saturday to catapult himself up the leaderboard as he looks to follow in the footsteps of Padraig Harrington, the last player to retain the Claret Jug a decade ago.
The 14-times major winner started poorly with a bogey at the second where he pushed his tee shot to the right and then narrowly missed the huge gallery following his match with a recovery that squirted low out of the rough.
On a day when some of the game’s less famous outscored the big names, Kisner earned a one-stroke lead over long-hitting fellow American Tony Finau and South Africans Erik van Rooyen and Zander Lombard.
The 42-year-old American, absent from the sport’s oldest major since missing the cut in 2015, carded a level-par 71 which included enough glimpses of the old magic and fighting spirit to suggest a 15th major title on Sunday is not so fanciful.
Now 29, McIlroy is aiming to end a four-year drought without a major victory but the trend is towards the strong contingent from the United States maintaining a firm grip on the sport's biggest prizes.
Speaking at Carnoustie on Tuesday two days before the championship’s first round, Woods said the Open puts less emphasis on power, a good thing for a golfer entering middle age.
The former world number one watched last year's US Open at Erin Hills from afar, still in the early stages of his recovery from spinal fusion surgery and unsure if he would resume his golf career.
Woods, the 14-time major champion, had a 36-hole total of six-over par 148.