Forward Cheney completed a swift move with a well-timed header and Buehler fired in with 14 minutes to go to give the team with the highest average age of players a winning start against the youngest team in the June 26-July 17 tournament.
"You play your first 45 minutes in a World Cup and after those 45 you start knocking the ball around a bit better. We did a good job," U.S. coach Pia Sundhage told reporters.
"It's good to have this result because it is so much easier going forward."
It was the fourth time the two sides had met at a World Cup group stage with the United States, twice world champions, having won two and drawn one of their previous three games.
On a sun-drenched afternoon in Dresden, the Americans looked livelier from the start and Carli Lloyd had an early chance when she connected with a Christie Rampone free-kick but her header was too weak to trouble keeper Hong Myong Hui.
Three-times Asian champions North Korea battled hard to stifle any American attack outside the box and made the most of their opponents' erratic passing game to venture forward.
American keeper Hope Solo had to come to the rescue twice late in the first half, palming away a Korean shot and intercepting a low cross from Song Jong-sun who was wreaking havoc with Ra Un-sim down the right wing.
WRONG FOOTED
The Koreans were lucky not to go a goal down early in the second half when Abby Wambach and 23-year-old forward Cheney each saw their efforts sail just wide as the Olympic champions stepped up a gear.
The two players combined beautifully in the 54th minute with Wambach sailing in a cross to the far post and Cheney made amends for her previous miss with a well-placed soft header that wrong-footed the keeper.
The Koreans almost struck back two minutes later with Ri Ye-gyong's 25-metre shot rattling the crossbar but apart from this solitary effort it was one-way traffic with the Americans cutting down on errors and pressing their rivals.
Buehler doubled their lead in the 76th minute, sliding and firing in a loose ball after it bounced off the bar.
Substitute Megan Rapinoe pounced on a keeper mistake in the dying seconds to put the ball in the net but her effort was disallowed for a foul on Hong.
Cheney had been a surprise starter instead of Rapinoe and was glad she had been given a chance.
"I worked my butt off and it worked," she told reporters. "I think either of us could have started today."
In the other Group C match of the day, Sweden beat Colombia 1-0.
