In the southern campaign launched by the British, Cornwallis lost a battle with the Americans under Nathaniel Greene at
A very odd phrasing. Greene lost every battle he fought with Cornwallis, however, he made the British pay a price it could not afford, weakening the British, until they ended up penned in Charleston.
In no battles, in my estimation, did Greene win. However, he won the war through making Cornwallis pay a stiff price for his victories, and Greene was the master at strategy, with significant troop movements that readied him for future engagements, at the expense of the British.
http://en.wikipedia.org/wiki/Nathanael_Greene