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Alex Schalk's header opened the scoring after eight minutes and Brian Graham's last-minute lob clinched victory.
But Kilmarnock were unable to change their fate in between as they slipped to an eighth home Premiership defeat.
They are eight points clear of Dundee United, who host Aberdeen on Wednesday, but have played two games more.
As soon as the second goal went in, dejected Kilmarnock fans among a paltry 2,633 crowd began to stream out of the ground, as the possibility of a relegation play-off - or worse - looms large.
Neither side was inhibited by their circumstances and the points at stake. The opening minutes saw them create a chance apiece, and that spell shaped the rest of the game.
The home side were first to impose themselves, but Greg Kiltie could not change his body shape quickly enough to properly connect with Josh Magennis's cross and he volleyed over as he rushed into the penalty area.
Kilmarnock would have been heartened by the opportunity, because their home form has been so consistently poor that the general mood at Rugby Park is a deep-seated anxiety. Even so, a familiar feeling of dismay swept round the ground soon after the Kiltie effort.
In County's first meaningful attack, Michael Gardyne delivered a cross into the penalty area from the left and Schalk slipped into space to glance a header into the far corner.
He was unmarked and had the time to compose himself, and that proved a costly aberration for Kilmarnock.
The goal invigorated Schalk. When another cross was sent into the area, he controlled the ball expertly with his back to goal, spun briskly and hit a shot on target that Jamie Macdonald had to move quickly to save.
Later in the half, he was about to strike another effort from inside the area when Kilmarnock centre-back Conrad Balatoni slid in to block.
The home side were initially unsettled by their lack of resolve in defence, but they did not concede their place in the game and kept fighting their cause.
It was typical of their misfortune, though, that Topi Obadeyi had to be substituted in the 30th minute because  of injury.
It was Obadeyi who came closest to scoring in the first half, with a tame header wide from Rory McKenzie's cross.
The interval provided Kilmarnock boss Lee Clark with an opportunity to revive his side. There was certainly a greater attacking intent to the home side's play in the second half and McKenzie swept a shot on target early on, only to see the Ross County goalkeeper Gary Woods save.
Kilmarnock saw plenty of possession, while County seemed comfortable defending their lines and striking on the break.
They almost added to their lead when Graham's cross was headed against the outside of he post by Liam Boyce.
In the closing minutes, Kilmarnock's organisation abandoned them, and Graham was able to steer a header over the stranded Macdonald to seal the victory. Booing from the home fans greeted the final whistle.
A hard-fought victory sent Ross County climbing to fourth place in the Premiership and increased the sense of alarm at Rugby Park.