Kirk, who took over at the top of the standings with his victory at the Deutsche Bank Championship earlier this month, fired a four-under-par 66 to join fellow American Billy Horschel atop the leaderboard in the PGA Tour's season-ending event.
Horschel, who climbed to second in the FedExCup points list by winning the BMW Championship on Sunday, emulated his playing partner Kirk by recording four birdies in a bogey-free display on a sunny but muggy afternoon.
Masters champion Bubba Watson also got to four under, having rebounded from a double at the 13th with three successive birdies, but he bogeyed the par-three last to open with a 67.
Also at three under in the PGA Tour's fourth and final playoff event were Australian Jason Day, whose caddie had to withdraw after seven holes because of a back problem, and Americans Patrick Reed and Jim Furyk.
Northern Irish world number one Rory McIlroy, hunting his fourth PGA Tour victory of the year, returned a 69 to remain in contention for overall playoff honours, a title he has never previously won and has specifically targeted this week.
Any of the top five in the points standings would clinch the FedExCup by winning the Tour Championship - and that quintet comprises top-ranked Kirk, Horschel (second), Watson (third), McIlroy (fourth) and Hunter Mahan (fifth).
Due to the threat of thunderstorms forecast for Friday afternoon, tee times for the second round have been brought forward by three hours.
(Editing by Frank Pingue)
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