Kyle Lafferty put the visitors ahead in the 18th minute, only for Billy Mckay to equalise seven minutes before half-time, and two goals in the space of three minutes shortly after the restart from Leo Hjelde and Mckay again had County in cruise control.
A 77th-minute penalty from Lafferty reduced the deficit to one, but Kilmarnock, who had Ross Millen sent off at the death, could not salvage anything in Dingwall as they slipped below Hamilton to the foot of the standings.
Lafferty showed his striker's instincts to open the scoring. Having seen his powerful long-range effort blocked, the ball ricocheting off a couple of players, he ignored the handball shouts of those around him, to fire the rebound into the net.
Mckay tapped home a brilliant cross from the right by Jason Naismith to bring County level and the Staggies burst into life at the start of the second half.
Within 70 seconds of the restart they were in front, with Naismith again the provider as he found Hjelde in acres of space to pick his spot and beat Colin Doyle for his first senior goal.
Kilmarnock had barely recovered before Mckay scored his second of the game, bringing down Jordan Tillson's ball forward and powering his shot into the net.
Mckay then had a shout for a penalty after being brought down by Brandon Haunstrup, but the referee waved those appeals away.
Euan Anderson did point to the spot at the other end with just under 15 minutes left on the clock, though.
Lafferty stepped up to score his second, but Kilmarnock could not find an equaliser to take a point back down to Ayrshire.
And their misery was complete when Millen was shown a second yellow card for dissent deep into added time.