A contest between two sides struggling for form was settled by a second-half goal from Ivan Sproule, who was later involved in an incident which saw United's Barry Douglas sent off.
Victory took Derek Adams' side to within two points of third-placed Inverness, although their fellow Highlanders have a game in hand.
Dundee United have won just once in seven games and are now five points worse off than County, but it might have been different but for a top-class Michael Fraser stop in the first half at Victoria Park.
The goalkeeper clawed out Jon Daly's diving header from Douglas' free-kick, though he would surely have been powerless had the big striker connected with a similar delivery later in the half.
The home side offered little before the break but were ahead nine minutes into the second half, Iain Vigurs leaving Scott Dillon for dead and standing up a cross which Sproule headed in from barely a yard.
The winger then went down heavily under a Douglas challenge which took both ball and man, earning the defender a straight red card.
County thrived with the extra body and twice came close to a second, Sproule teeing up Vigurs for a side-footer which missed narrowly and Richard Brittain hitting the bar late on.