Johnson, who drove the ball prodigious distances, posted a 16-under 203 total, while joint halfway leader Brian Harman remained in the hunt with a steady 69 to stand alone at 14-under on another breezy day at the Kapalua Plantation course on Maui.
Spaniard Jon Rahm played the final five holes in five under to match Johnson's 66 and trail by four shots.
"I drove it really well, obviously that's a big bonus around here, and I hit a lot of good iron shots and I feel like I'm rolling it well (on the greens)," Johnson told Golf Channel.
His eagle did not hurt his score either.
"I landed my shot perfect and it got on the green and tracked to the hole," he said of the shot, which he landed some 30 yards short of the cup and watched as he ball rolled down the steep slope and into the hole.
Johnson had been in similar imperious form early last season before he had to withdraw from the Masters following a fall down some stairs.
A bruised back kept him out of action for four weeks and by time he regained his form the majors had passed, and attention had turned to the likes of Justin Thomas and Jordan Spieth.
Johnson, however, is showcasing similarly good form in Hawaii and is determined not to repeat the experience of last October when he surrendered a six-shot lead in the final round at the HSBC Champions in Shanghai.
"That was just kind of a fluke day," he said.
"I was playing a new set of irons and I wasn't that comfortable with them. I'm a lot more comfortable with them now. I feel like I can control the ball very well.
"I've got a good game plan around here. I'm not going to play any different tomorrow."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
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