Tom Watson, the reigning Senior British Open champion, posted a 6-under-par 66 to share second place. Watson, who owns 47 wins combined on the PGA and Champions Tours, has never won in the state of Florida.
Watson was joined in second place at The Club at TwinEagles by Brad Bryant, Don Pooley and Rick Karbowski.
Gil Morgan, a two-time winner of this event, is one stroke further back at minus-5 and stands alongside Fuzzy Zoeller, Dan Pohl and Loren Roberts, who has won the first two Champions events this season.
Eaks, who is still in search of his first Champions Tour crown, got off to a quick start with a birdie on the first. He came back to birdie the third from 4 feet out and the fifth to quickly get to minus-3.
The 53-year-old made it two in a row as he got up and down for birdie on the par-5 sixth. Eaks parred six straight holes around the turn. He then drained a 38-foot eagle effort on the par-5 13th to jump to 6 under.
Eaks, who also shared the lead after the first round here last year, parred each of his next four holes to remain there. He moved one stroke clear of the field with a birdie on the last.
'That was a very solid round of golf,' Eaks said. 'I am trying to hit it softer and hit more fairways. I hit 40 percent of my fairways last year. I have a better chance of winning hitting it in the fairway and not quite as long.'
Watson got on the board with an eagle on the par-5 third. He then picked up birdied on Nos. 5 and 7 to get to 4 under. Watson drained his next birdie on the 10th. He moved within one of the lead with a birdie at the 15th, but parred out to remain there.
'The scoring conditions were ideal with no wind. I played well today,' said Watson. 'I've finished second a bunch of times in Florida, but I really can't explain not winning in the state.'
Bryant ran off three birdies in a four-hole stretch from the fourth. After dropping a stroke on the eighth, the 51-year-old birdied No. 9 to turn at minus-3. Bryant birdied the 11th and 13th to keep moving up the leaderboard. He grabbed a share of second with a birdie on the 17th.
Pooley played the first five holes at even par, with two birdies and two bogeys in that stretch. He managed to make the turn at minus-2 with birdies on the sixth and ninth.
Around the turn, the 2002 U.S. Senior Open champion posted back-to-back birdies from the 12th and then again from the 16th to share second.
Karbowski was 4 under through four holes, with two birdies and an eagle. He bogeyed the fifth, but got that shot right back on the sixth. After a bogey on No. 10, Karbowski birdied the 11th to get back to minus-4. He birdied the 13th, then claimed a share of second thanks to a birdie at the last hole.
Bruce Summerhays and Dana Quigley lead a group of players tied for 10th at 4-under-par 68. They were joined there by Keith Fergus, John Jacobs, Peter Jacobsen, Tom Jenkins, Massy Kuramoto, Jose Maria Canizares, Mike San Filippo and Des Smyth.
Defending champion Mark James is tied for 54th after opening with a 1-over-par 73.