The Klingons would seem to have possessed a technological head start over the Humans, having been a warp culture longer. They may have kept this advantage, as the Humans and the Federation advanced so did the Klingons. Maintaining a comfortable lead through the centuries.
During the Dominion War, in the Second Battle of Chin'toka, one of the Klingon ships had previously made a adjustment to the ships power system that (unknown at the time) rendered the ship invulnerable to a Breen weapon. The Klingons quickly figured out the reason they survived and changed the power systems on all their ships. An engineering fix, to a combat problem.
It can't be simply using the technology left to them by the Hur'q, with no innovations of their parts. Otherwise the Klingons would be stuck with the same technology we first saw them with in the 22nd century.
The Klingon culture may venerate it's warriors, but it's the Klingon aristocracy (and not the warriors) that runs the Empire.