Woods was five shots adrift of Hoffman at the halfway mark and declared he was "still in it" in his first competitive tournament for 10 months after recovering from a fourth back operation.
England's Justin Rose (71) and Jordan Spieth (72) were tied for second at nine-under 207, one stroke ahead of Italy's Francesco Molinari (71).
Much like Tiger Woods' kids, the young and upcoming lot of world golf has only seen the 14-time major victor compete on television or Youtube. However, those odds were quickly trimmed as he got off to an encouraging start.
Woods, making his first start since withdrawing from the Dubai Desert Classic in February, went out in 35 shots with two birdies and a bogey, before returning in 34 shots with three birdies and a bogey. Woods was 1 over on the back nine with one birdie and two bogeys and now sits five shots off the lead at 7 under.
The 41-year-old's round could have been better were it not for a bogey on the par-5 15th hole.
"I did not know what I could do", admitted Woods.
"The only thing I struggled with was the speed of the greens". "I've been playing a lot of holes at home but it's different when you are in a tournament".
"Tiger is back", Carter said of Woods' Thursday performance.
Fleetwood, who is making his debut in the event before getting married in the Bahmas on Tuesday, was bogey-free as he took a one-shot lead over American duo Rickie Fowler and Matt Kuchar.
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