This sounds a lot like the Christopher Anvil short story Pandora's Planet which was later expanded into the novel Pandora's Legions.
The basic concept you mention about humans outsmarting the invading aliens is expressed by the following summaries:
"The mighty Centran Empire had been conquering star systems for centuries -- and then they took on Earth. And in spite of their more advanced weapons, the Centrans weren't sure just who had conquered who."
"Pandora's Legions has a cleaver concept for its plot. A galactic empire has invaded Earth. The only problem for them is that other than having the ability for space travel, their technology is no more advanced than roughly 18th Century Earth; and that the Earth's inhabitants seem to be a lot smarter. The book tells the story of what happens when these seemingly hapless aliens get out classed by us lowly "Earthmen". "
Then the aliens get the idea of sending humans out to fight:
Thrift Book review
A classic Christopher Anvil type story and quite fun to read.