Woodland birdied six times on Friday and finished nine-under, two shots ahead of second-place Rose. Woodland did not bogey a single hole.
Rose shot 1-under-70 on Friday and is seven-under for the tournament. He ended play with a two-shot lead over Aaron Wise before Woodland took a late lead.
Woodland has never won a major. His sixth-place finish at the 2018 PGA Championship is his best result in a major tournament.
Louis Oosthuizen ended Friday in third place at six-under. Wise and Rory McIlroy are tied for fourth at five-under. Two-time defending champion Brooks Koepka is among five players tied in sixth place at four-under.
The cut was two over par.
Rose posted consecutive sub-par scores in the tournament for the first time in his career. He said he was happy with his performance but still had "no expectations" for the weekend.
"I just like my position, the course and the way I'm trending," Rose said.
Rose carded a 65 on Thursday. That equaled the lowest round in a U.S. Open at Pebble Beach since Tiger Woods, who accomplished the feat in 2000.
Woods won the tournament that year. Rose won the U.S. Open in 2013 and is looking for his second career major win.
"I still don't feel like I'm cooking and I'm going to need to find that [extra] gear if I'm going to hoist some silverware on the weekend," Rose said.