In other matches, China beat Britain 2-1 to stay in the running for the semis, Australia beat South Africa 1-0 to go to the top of its group and Belgium drew 1-1 with Japan.
South Korea opened the scoring against the Netherlands with a fifth-minute field goal from Cheon Seul-ki, but Lidewij Welten equalized for the Dutch side five minutes later.
The Dutch went ahead on goals by Carlien van den Heuvel and Ellen Hoog either side of halftime and South Korea forward Cheon scored again from a penalty corner with six minutes left to keep pressure on the Dutch side.
But the Netherlands' defence held and the side won its fourth match in a row to guarantee that the side will finish first or second in its group.
"I think it was good for us that they scored (first), as after that goal we gave so much energy and we were so creative ... I think we were the better team today," Dutch forward Kim Lammers said.
New Zealand took over first place in its group and the Americans are in fifth place in the six-team group.
The U.S. twice came back from one-goal deficits. New Zealand captain Kayla Sharland netted an early goal from a penalty corner and Gemma Flynn scored in the 19th minute.
Katie O'Donnell and Claire Laubach scored the U.S. goals that twice levelled the match, until the 64th-minute Kiwi winner from Clarissa Eshuis.
"We're a bit disappointed. We had obviously hoped to finish a little higher," U.S. captain Lauren Crandall said.
"We're happy with some of the play we've done. There are spots that we definitely need to improve on, and we'll look to do that, but right now it's just coming out to South Africa, making sure we bring our game."
China ended Britain's three-game winning streak. Fu Baorong and Zhao Yudiao scored from penalty corners in the second half and Britain's only goal came in the last minute by Crista Cullen.
"We haven't beaten Great Britain for the last two years, and we have beaten them here," China coach Kim Sang-ryul said. "We played very aggressively — the match was our last chance."
Britain did not make the most of four consecutive first-half penalty corners. The host team faces reigning Olympic champions the Netherlands on Monday.
Kate Walsh returned as Britain's captain after being out with a jaw injury.
"We all feel very disappointed with the result and the performance," she said. "We know we can play better than that. We talk about about the 'gold' mentality — that's how we go into every game. That's the standard we set ourselves."
Jade Close scored the only goal of the Australia game with an eighth-minute field goal. Neither side could take advantage of nine penalty corners to add to the scoring.
South Africa attacked the Australian circle 27 times, nine times more than South Africa.
"It was definitely the strategy to put a lot of pressure on Australia, and it worked well," South Africa forward Pietie Coetzee said. "Unfortunately we just could not finish it off."
Captain Yukari Yamamoto scored in the 58th minute from a field goal to give Japan its draw with Belgium. Jill Boon had given Belgium the lead from a penalty corner at the end of the first half.
Japan and Belgium are at the bottom of their group and will not advance to the semifinals.