Depending what you consider "American" and invading "power", American has been invaded several times.
1942- 1943 The Imperial Japanese Army occupied the island of Attu. One of the Islands in the Aleutian chain most. It was part of the territory of Alaska.
The US reclaimed the Island after heavy fighting.
http://en.wikipedia.org/wiki/Battle_of_Attu
The last serious hostile power to invade the mainland US was the Confederate States of America during the US civil war. The CSA was never observed by the US as a state, so they are considered a hostile power.
The last time a hostile power invaded US soil was in 1911. When Panco Villa Mexican revolutionary invaded the US raided a small town.