After a frustrating front nine, Woodland kicked off his birdie run with a chip-in at the 11th, and later capped his day with another birdie at the par-five 18th to move to 12-under 134 at the Kapalua Plantation course on the island of Maui.
Northern Ireland's Rory McIlroy shot a 68 for a share of second place on nine-under alongside Bryson DeChambeau (68) and Kevin Tway (71).
Woodland, who has won three times in 231 starts on the PGA Tour, said his patience had been tested on a day that started extremely windy before abating somewhat as the leaders negotiated the back nine.
"It was frustrating early," Woodland said. "The wind was really messing with me on the greens. I regrouped after missing a short one on nine, chipped in there (on 11) and got it rolling."
McIlroy, in his first start at Kapalua, enjoyed getting to grips with the conditions, a five-foot miss at the 15th notwithstanding.
"I've enjoyed last couple of days, flighting different shots, hitting different trajectories," he said.
"With all the technical work I've done in the off-season it's a real contrast to come out here and completely forget about the swing and just hit the shot."
Overnight leader Tway, who shot a 66 on Thursday despite suffering a sinus infection and ear ache, said he felt much better after sleeping more than 12 hours, though his second round was five shots worse than the first.
Tway at least fared better than Johnson, who pulled his drive into a penalty area at the fourth and was then directed to his ball by a marshal.
Johnson chopped back into play, only to come across his own ball a few yards further on.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford )
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)