Despite the home side controlling possession early on, it was County’s Graham Carey who forged the game’s first opportunity, forcing Kilmarnock’s Craig Samson into an early save.
Kilmarnock’s Josh Magennis then had an effort saved by Mark Brown before Mark Connolly went close with his header from the corner of the six-yard area.
But it was County who opened the scoring when Carey fired the visitors in front from outside the box after 33 minutes.
They doubled their lead seven minutes later when Michael Gardyne drilled the ball home from the centre of the area.
Connolly had another header for the home side which went marginally wide before Paul Quinn added a third for County, with Carey this time turning provider.
Kilmarnock looked reinvigorated after the break with Rory McKenzie and Robie Muirhead both going close.
But County still looked threatening and Jackson Irvine had a shot at goal before Miller had a pair of headers that failed to find the target.
Connolly and Magennis both drew saves from Brown as the home side tried to find a way back into the contest but it was to no avail as Ross County registered just their second league win this term.