The world number one kept his three-peat bid alive with a bogey-free three-under par 68 on Saturday that included a par save from the fringe at the 15th and a par from behind the cypress tree in the 18th fairway.
Having come from five shots back to win at Shinnecock Hills last year -- becoming the first player since Curtis Strange in 1988-89 to repeat as US Open champion -- he was quietly confident he could get past Woodland and Justin Rose, who went into the final round one shot off the lead.
"I have to stay patient and keep doing what I'm doing," Koepka said. "If you’re within three strokes on the back nine anything can happen."
Willie Anderson, the Scottish immigrant who was the first of four golfers to win four US Open titles, is the only player to lift the trophy three straight times -- in 1903, '04 and '05.
Six players have since won two straight but fallen short in a third.
But the weight of 114 years of history balances lightly on Koepka's big frame.
"I just enjoy the pressure," said Koepka, who won his second straight PGA Championship title last month at Bethpage Black to take his tally of major titles to four in his last eight major starts. "I enjoy hitting good golf shots when the pressure is on."
Koepka isn't the only marquee name poised to pressure Woodland, a three-time winner on the US PGA Tour who is seeking his first major title.
Along with England's Rose, the 2013 US Open winner and a former world number one, there's former British Open champion Louis Oosthuizen in a group at seven-under that also includes Chez Reavie and four-time major-winner Rory McIlroy at six-under.
Pebble Beach, soft and receptive in cool, damp weather on the Monterey Peninsula, has yielded a wealth of low scores over the first three days, including the first- and second-round 65s posted by Rose and Woodland which matched the lowest ever shot in a US Open at the famed seaside course.
With the greens firming up and tougher pin positions Pebble Beach promised to offer the test of skill and fortitude the US Golf Association strives for on Sunday.
"The greens are so small, and when it gets a little firm like this and they start to tuck pins in little corners, it's angles, it's all angles," McIlroy said. "You're trying to think and move ahead.
"It's a little bit like chess where you're crossing paths, going from the third green to the fourth tee and seeing a group tee off 17 and watching their balls land on the right side and kicking in. You have to anticipate what your ball is going to do along the ground, as well.
"You can't go firing at pins because you're going to one-hop it over the back all day."
That's why Koepka was most pleased to have kept any bogeys off his card on Saturday.
"I think that's important," he said. "I feel like eventually these birdies have to come.
"I don't need to go out and chase. If I can just make a few putts, I could be right there."