Wambach scored her 141st goal in her 185th appearance for her country in front of a 29,522 crowd at Old Trafford in Manchester.
It was enough to guarantee the United States top spot in Group G, and a quarter-final clash with either Canada or the third-placed team from Group E at Newcastle's St James' Park on Friday.
The first half was comprehensively one-sided for Swedish coach Pia Sundhage's USA team against a DPR Korea outfit hammered 5-0 by France in their previous game.
It took the USA until the 25th minute to break the deadlock, with goalkeeper O Chang-ran denying Megan Rapinoe and Alex Morgan, with the latter also striking the post.
The opener when it came was well crafted, with Carli Lloyd feeding Morgan in the area who turned inside her marker to lay the ball off for Wambach to beat O from seven yards.
Wambach later forced a third good save from O and also saw another effort hit the left-hand upright before the break.
Beyond that the second half was only notable for Choe Mi-gyong's 81st-minute dismissal for two yellow cards within five minutes.
Elsewhere, Elodie Thomis fired France into an Olympic quarter-final showdown with Sweden after a narrow victory over Colombia.
The winger's early strike was enough to claim the points, although a resilient display by keeper Sandra Sepulveda and a second-half Colombian fightback ensured the result remained in doubt until the final whistle.