It took three late goals for Dundee to secure the points in a match the Dark Blues comprehensively dominated.
Former Dundee player Hugh Robertson handed Ross County the lead with a low left-foot drive from 12 yards.
The home side equalised when player-manager Alex Rae struck a fierce left-footed drive from 20 yards.
Derek Lyle put Dundee ahead with a close-range finish before Andy McLaren sealed an impressive performance with a fine strike form the edge of the box.
Dundee: Roy, Gary Smith, Dixon, Rae, Strong, Mann, Kevin McDonald, Robertson, McLaren (McGinty 86), Lyle, Campbell (Deasley 70). Subs Not Used: Boggan, Gates, Calum McDonald.
Goals: Rae 73, Lyle 77, McLaren 84.
Ross County: Samson, Gary Irvine, McKinlay, Dowie, Webb, Scott, Gardyn, Adams, Crooks (Hooks 73), Gunn (Caimi 77), Robertson. Subs Not Used: Malin, McCulloch, Moore.
Goals: Robertson 65.
Ref: M McCurry