County's Jonathan Flynn fired wide just before Dundee's goal, which came 25 minutes from the end.
Leighton Mcintosh converted from close range to leave County level with second-bottom Cowdenbeath, who have an inferior goal difference.
Ross County: McGovern, Miller, Flynn, Kettlewell, Boyd, Fitzpatrick (Morrison 84), Gardyne, Craig (Smith 79), Vigurs, Barrowman, Milne (Wood 75). Subs Not Used: McCarthy, Marr.
Dundee: Douglas, Irvine, Lockwood, McKeown, Benedictis, Weston, Riley, Harkins, Forsyth, O'Donnell, Mcintosh (Rennie 88). Subs Not Used: Gibson, Bartlett, Webster, Tulleth.
Goals: Mcintosh 65.
Att: 3,205
Ref: Anthony Law
Source: BBC Sport
Source: BBC Sport