Simpson matched Matthew Fitzpatrick with a 6-under 66 at The Concession in the World Golf Championships event moved from Mexico City to Florida because of COVID-19 circumstances.
Simpson's finishing stretch included a wedge to 2 feet, a 30-foot birdie putt on the 16th hole and a two-putt birdie from about 40 feet on the par-5 17th.
Fitzpatrick, who contended last week at Riviera, played bogey-free on the Jack Nicklaus design that had never been used for a PGA Tour event.
"Very pleased with the start," Simpson said. "I worked on a couple things last week with putting alignment and with my driver and I saw good things from that today. You always want to see it first round back, but it doesn't always happen that way, so I was happy to see like tough tee shots with trouble, really stepping up and making good swings.
"And made a lot of putts today," he added, "so that was a good feeling."
Johnson had his first Sunday round over par in a year when he shot 72 last week while in contention. The start at this World Golf Championship was even worse.
The world's No. 1 player drove left into the trees on the 18th hole as he was making the turn, had to pitch out sideways, came up short and then failed to get up-and-down to take double bogey. He made another double bogey on No. 5 with a tee shot into the water.
Johnson wasn't alone in his struggles. DeChambeau also shot a 77, with his big trouble coming on the 16th. After a tee shot into the water, he went right of the fairway, came up short of the green and took 3 shots to get down for a triple bogey.
"If you're on, you're going to have chances. You're going to be really good with the tee ball or you're going to have chances with your iron play," Horschel said. "If you're off with your ball-striking and you miss in some tough spots, you can look pretty silly."
Second-ranked Jon Rahm bogeyed the final hole late in the afternoon for a 68.
Rory McIlroy had three bogeys in a 69.
"I think with any new course it's just a matter of getting comfortable with visuals and lines off tees, and then I think we're all sort of learning the golf course a little bit as we go along," McIlroy said. "Most tour events we go to, we basically know where the four pin positions are going to be and we can practice to those.
"I think tee to green, it's pretty simple," he said. "But then around the greens, I think it's one of these places, the more you play it, the more you'll just feel comfortable with it."
Third-ranked Justin Thomas one-putted his last four holes -- three birdies and one par -- to salvage a 73 after he had dropped 4 shots in a three-hole stretch on his first nine. The par was a 10-footer on the par-5 seventh after it took him 2 shots to get out of a fairway bunker.
Homa, coming off the hometown win in Los Angeles, also had a 73.
Patrick Cantlay, who leads the FedEx Cup, withdrew before the start of the round with stomach and dehydration issues.