Clarke rattled off nine birdies in his opening round at Norwood Hills Country Club on Friday (local time), three of them coming over the last five holes after he doubled the par-4 13th.
At seven-under-par 64, he is one stroke ahead of Hensby and two in front of Americans Vaughn Taylor and Tim Petrovic.
Hensby had four birdies on his front nine and two after the turn to card a six-under 65 and be outright second.
The 58-year-old Clarke, who has six PGA Tour Champions wins to his credit, came into the playoffs 12th in the standings. He's projected to move up to fifth if he wins the first of three playoff events, while Stewart Cink could maintain a healthy lead. Cink is currently fifth on the leaderboard at four-under 67, three behind Clarke.
The top 72 players in the regular season qualified for the playoffs, and the top 54 in the standings after this week advance to the Simmons Bank Championship.
Hensby sits in 62nd and has an opportunity to rocket up those standings if he continues to play how he played on Friday.
However, he revealed after his round that he has booked a trip back to Australia and doesn't intend on missing it, even if he advances in the playoffs.
"I think my time's done out here," Hensby said after his bogey-free 65. "I've enjoyed it. I've not really - let's just say I've had enough and I want to spend time at home.
"Obviously if I win (this tournament), then at the end of the day, next year if I felt like coming out in the summertime, which I won't be out here but if I did come out, it would be in the summertime.
"But yeah, I'd like to have that choice so to speak, I guess. But in saying that, there's a long way to go."
Of the other Australians in the field, Greg Chalmers and Steve Allan are both at three-under, a shot clear of David Bransdon, Richard Green and Michael Wright.
Stuart Appleby is one over, while Cameron Percy and Mathew Goggin are both even with the card.
Rod Pampling opened with a four-over 75, with Scott Hend two shots further back.
