Jon Guthrie's header after 64 minutes proved to be the only goal of a scrappy game and helped lift Gary Holt's men up to 10th spot.
County, who barely created a chance of note, lost Carl Tremarco to a red card for a second booking early in the second half.
Livingston made three changes from the team beaten by Aberdeen at Pittodrie in their previous match. In came Efe Ambrose, Julien Serrano, and Lars Lokotsch, with Jack Fitzwater, Jack McMillan and Jason Holt dropping out. There was no place in the matchday squad for new signing Anthony Stokes.
County, in turn, made two changes to the starting line-up following their 1-1 draw with St Mirren. Harry Paton and Josh Reid dropped to the bench, their places taken by Tremarco and Keith Watson.
The home side enjoyed the first chance of the game and really ought to have moved in front. Nicky Devlin sent over an enticing ball from the right and Scott Pittman somehow scooped it over the bar from six yards.
It was a first half of few chances. Iain Vigurs fired in a long-range kick for the visitors that was easily held, while Lokotsch miscontrolled the ball in the box in a rare scoring opportunity for Livingston.
The German almost atoned before the interval. Alan Forrest crossed from the right and Lokotsch's header beat goalkeeper Ross Laidlaw but struck the top of the crossbar.
County could have got their noses in front right before the break but Billy McKay's header from a Vigurs corner drifted just wide of target.
The visitors' task got tougher just seven minutes into the second period. Tremarco caught Devlin late outside the box and referee John Beaton did not hesitate to show him a second yellow card.
County made two substitutions and switched to a 4-4-1 formation to try to stem the Livingston pressure, but chances still came and full-back Serrano had a volley well saved.
The Frenchman was involved again when the home side moved in front after 64 minutes, sending in a cross after a short corner that was headed in by Guthrie from close range.
Livingston kept pushing for a second and substitute Jason Holt had a low drive well saved by Laidlaw.