Sluman, who needed a sponsor's exemption to gain entry into the tournament, started quietly with three pars but then birdied six of the next nine holes and added one more on the 15th for a bogey-free start at the $5.2 million event and a one stroke advantage on South African Rory Sabbatini.
Being a frontrunner has never really suited the 1998 PGA Tour champion, who has held the first round lead 12 times in his career but has never gone on to win the event.
"Obviously I was pleased with how I played today, but I'd first like to thank the tournament committee for inviting me," said Sluman.
"I needed a sponsor's exemption this year for the first time in a long time and without them considering me, I certainly wouldn't be here, I'd be watching this on television back home in Chicago."
Sitting one stroke back at five-under 67 is a group of eight golfers, including Australians Adam Scott and Nick O'Hern, while Woods headlines another large group at three-under 69.
Playing for the first time since his record streak of 142 consecutive cuts at U.S. PGA Tour events came to an shuddering end at the Byron Nelson championship three weeks ago, Woods was back in solid form opening with a tidy bogey-free
The U.S. Masters champion opened with 10 straight pars holes before mounting a charge with three late birdies.
Woods' two great rivals here got off to far less impressive starts, world number one Vijay Singh slumping to a five-over 77 and defending champion Ernie Els carding a one-over 73.
"With the wind blowing like this, extremely happy," said Woods, assessing his performance. "Made no bogeys, three birdies and that's it.
"Very solid, I guess. I didn't really do anything all that wrong, did a lot of things correct today and placed the ball where I needed to place it."
Playing at the event he hosts on the course he designed, Jack Nicklaus had looked ready to card a solid opening round sitting on even par through 14 holes.
But the 65-year-old staggered to the finish with bogeys on three of his final four holes for a three-over 75 and his dream of making the weekend in jeopardy.
"I almost scared myself today, I had a chance to shoot a pretty darn good score," lamented Nicklaus, who played with Els and David Toms. "Even after I double bogeyed the third hole, which was kind of crazy.
"Then the last three holes I limped in with a couple of bogeys at 17 and 18, which are pretty hard holes. I had a chance to play pretty decently. I shot 75, that's about my game."