Lee Wilkie rose above the County defence to head home the opener in the 36th minute and substitute Johnny Russell scored a killer second 13 minutes from the end.
The hosts' woes were compounded seven minutes from time by the dismissal of Martin Scott.
United forced the first corner of the match in the fifth minute but Craig Conway's inswinger was headed clear by defender Gary Miller.
County found it difficult to get a hold of the ball in the early stages and had to wait until the 17th minute when Michael Gardyne tried a long-range shot, but it flew well wide of Steven Banks' right-hand post.
Both sides were trying to get the upper hand with play restricted to the middle third.
In a breakaway move in the 17th minute, Michael Kovacevic tried his luck from distance but sliced his shot well off target.
County threatened five minutes later when Steven Watt sent Scott Morrison free on the left and the full-back's cross was touched away from under the crossbar by Banks before it was cleared.
The home side were growing in confidence and Gardyne had Banks at full stretch to push away a powerful effort.
County were almost in after 33 minutes when another Morrison delivery came off Andy Webster but when the ball broke to Craig he fluffed his shot and the ball went wide.
United responded by forcing a couple of corners in quick succession. Danny Cadamarteri headed Conway's first corner wide in the 34th minute but a couple of minutes later Wilkie towered above the County defence to power the second into the corner of the net.
The visitors opened up the County defence a couple of minutes from the break when Cadamarteri cut the ball back for Scott Robertson but his shot from just inside the area was blocked by Watt.
United went straight into the attack and forced a corner on the left. Conway's kick found Wilkie at the back post but the big centre-back failed to control the ball and it went behind for a goal-kick.
In a flurry of activity at the other end, Craig was then twice denied by the woodwork.
Webster lost the ball on the edge of the area and Craig's rising shot clipped the top of the crossbar. United failed to get the ball away and Craig had another chance when they ball fell to him eight yards out but he lashed against the base of the post.
United's Jennison Myrie-Williams was booked for simulation inside the County box by referee Craig Thompson in the 60th minute.
County kept plugging away and a Craig delivery from the by-line was met by Richard Brittain at the far post but his shot was blocked at point-blank range by defender Paul Dixon.
And it was all over in the 77th minute when United doubled their lead.
County defender Alex Keddie failed to deal with a pass back from Morrison and the ball broke to United substitute Russell, who raced clear on goal and slipped his effort past the advancing McGovern.
It got worse for County the six minutes later when Scott saw red for a wild challenge on Conway.
Russell was looking a real threat and he had another effort on goal in the 84th minute but McGovern saved well.