Noren and Simpson both carded four-under par 66 at PGA National in Palm Beach Gardens, Florida, where only 20 players broke par.
Although he didn't manage to join that group, Woods called it the best ball-striking round of his latest comeback, which has included a tie for 23rd at Torrey Pines last month and a missed cut at Riviera in Los Angeles last week.
"I'm very pleased," said the 14-time major champion, who had three birdies, a bogey and a double-bogey.
"The wind was playing really hard, the rough's up and it's really tough to make putts out there."
Nevertheless, Woods matched his best opening round in four appearances at PGA National.
His decision to play in Florida this week marks his first attempt at back-to-back tournaments since 2015 as he vies to become a contender again in the wake of spinal fusion surgery last April.
Woods teed off on the 10th and had two birdies and a bogey in his first nine holes.
"One bad hole today," Woods said. "That's the way it goes."
He responded immediately with a birdie, splitting the fairway at the sixth with a two-iron and draining a six-foot putt.
"I felt like I had good touch, but more importantly, I made a lot of the key short putts for par," Woods said. "It was really tough. Some of those putts were a little bit bouncy."
Noren, a nine-time winner on the European Tour, who fell to Jason Day in a marathon playoff at Torrey Pines, grabbed the last of his five birdies at his final hole, the par-four ninth to be the first in the clubhouse on 66.
Simpson had three of his five birdies on the front nine. His last came at the tough par-three 17th, where he rolled in a 30-footer to bounce back from his only bogey of the day.
"I'm definitely excited to get a good round under my belt," Simpson said
Former British Open champion Louis Oosthuizen of South Africa, reigning USPGA Champion Justin Thomas, Daniel Berger and Mackenzie Hughes were a stroke off the lead on 67, with Dominic Bozzelli, Jamie Lovemark, Russell Henley and Ben Crane tied on 68.
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