Runner-up at Bay Hill last year, 2023 US Open champion Clark best handled the tricky conditions at the Orlando course, with the wind playing havoc.
With a prize purse of $A31 million, Clark's five-under-par 67 was one of just 14 rounds under par out of the 72-man field in the signature event.
Fellow American Keegan Bradley, Canadian Corey Conners, Irishman Shane Lowry and South Africa's Christiaan Bezuidenhout are in a four-way tie for second.
Davis, who posted a two-under 70 alongside new world No.2 Northern Ireland's Rory McIlroy, is in the next group as well as Korean Si Woo Kim and Englishmen Justin Rose and Max Greyserman.
World No.1 and defending champion Scottie Scheffler looms a further shot back.
Adam Scott carded a three-over 75 to be tied for 33rd while Jason Day, who won the tournament in 2016, a shot further back.
Fellow Australian Min Woo Lee is in danger of missing Friday's cut after opening with a disappointing six-over 78.
Clark made the turn in three under par and made a short birdie putt at the 13th, a two-putt birdie at the par-5 16th and a tap-in after a tight approach at the final hole.
"I knew it was going to be really challenging," Clark said.
"I was really just trying to keep it in front of me. Anytime I got out of position, hit it back short of the green, leave myself into the wind, easy chips.
"I really didn't have that much stress, which was really nice."
Sydneysider Davis had birdies at the third and fifth and rode a rollercoaster on the back nine with three birdies and three bogeys, including one on the 18th.
The world No.49 said he felt a putt away from being amongst the front-runners but was ultimately happy with his round - and his start to the year.
He's had three top 20 PGA tour finishes including fifth in the prestigious AT & T Pebble Beach.
"I feel like for me personally five (under) was right there - it was just a matter of an up-and-down and a nice putt away from being five or six under ... I felt like I could have easily just as easily done that today," the 30-year-old said.
"At the same time, it is tough to keep a round going when it's like this ... it was breezy, gusty, it was a little tough to pick the wind at times.
"I hit a lot of really good, high-quality shots, made a couple of nice putts, for the most part kept the round really clean.
"There's a lot of good players here, so I'm very happy with two-under."
