Bryan hit consecutive tee shots into the hazard - including on the par-3 15th, leading to double bogey - and he birdied the 18th to salvage 72 and sit six shots back.
Hatton did his work before that stretch, running off three straight birdies to get within one of the lead.
England's Tyrrell Hatton is Fowler's closest competitor. But I think [my caddie] and I have talked about it before, and the way things went in Abu Dhabi; when you do have that cushion, it gives you the opportunity to accept mistakes. "There were times when she said I should have gone and played".
Powered by steady play, the Honda Classic is Rickie Fowler's to lose on Sunday. But he went long on the 17th and was perplexed by the Bermuda grass that he rarely sees.
For just the third time since the Honda Classic moved to PGA National 11 years ago, it appears the victor will reach double digits under par. He still made bogey.
However, if Hatton were to finish runner-up he would earn enough, and some $US 700,000, to be afforded "Affiliate" membership and thus be presented with a fuller 2017 PGA Tour schedule. Hatton pulled within one of taking over the lead, powered by three birdies in a row, but a bogey on the 17th and par on the 18th left him trailing at 9-under.
Scott won last season despite a quadruple bogey on the par-3 15th hole in round three.
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Hatton, whose five victories as a professional include a European Tour win at the Alfred Dunill Links Championship past year, was just one stroke adrift after birdies at the 12th, 13th and 14th.
Hatton is competing this week on an invitation and in his first event of seven tournaments he will contest in the United States and Mexico up to an including the May 11th commencing Players Championship. His last PGA Tour win was in September 2015 at the Deutsche Bank Championship.
"I feel like it's time for me to start finishing off some more events when I am in this position, " Fowler said.
"I was able to score well and manage it well and scramble well early on to keep the momentum going", Fowler said.
The confident 25-year-old added a 67 to his opening 68, while compatriot Donald was also three under for a day which started brightly when he holed his 161-yard approach to the 12th for a stunning eagle-two. But on Saturday, he made no birdies, shot 74 and dropped out of the hunt.
"The week before, I don't know if he got lucky there, too", Berger said of Thomas' win at Kapalua. So I didn't really try and put more pressure on myself to play better or perform like a No. 1.