Jamie Reckord scored the only game of the game at the Global Energy Stadium as County ended Dundee’s unbeaten run of eight matches.
County had three great chances to score before they got the vital goal, including an effort from Jackson Irvine which Dundee goalkeeper Scott Bain touched on to the post.
County kept the faith in the same line-up for the third match running, while the visitors named Gary Harkins in place of Paul McGowan in the starting line-up in the one change from the side which beat Motherwell last Saturday.
The first half lacked any clear-cut chances, Dundee’s Greg Stewart blazed wide with a long-range effort while Michael Gardyne flashed his shot wildly over the crossbar with the goal at his mercy.
County went all out for an opener at the start of the second half but Scott Boyd saw his close-range shot blocked by Scott Bain.
The home side were getting closer and Bain did well to touch a low drive from Irvine on to the post in the 55th minute before rushing out to clear from the onrushing Australian.
However, the hosts’ pressure paid off in the 66th minute when Boyce fed the ball through for Gardyne, who shrugged off his marker and chipped the ball to the back post for Reckord to tap home.
It was almost a second for County in the 77th minute when substitute Jake Jervis got on the end of a De Vita cross but his header crashed off the underside of the crossbar before being cleared.
Dundee pushed for an equaliser but they never came close to testing Brown in the County goal before the end.