A Sean O'Connor piledriver on the stroke of half-time earned Queen of the South a Scottish Cup replay.
The home side took the lead after 37 minutes when former Queens striker Derek Lyle headed in his seventh goal of the season.
With half-time approaching, the Dundee defence hesitated and O'Connor popped up to rifle home an angled finish.
Despite enjoying the majority of possession in the second half, the home side made little of it.
Dundee: Roy, Griffin, Mann, MacKenzie, Dixon, Harris, Rae (Campbell 76), Shields, Robertson, Lyle, Swankie (Clark 84). Subs Not Used: Reidford, Johnson, Forsyth.
Booked: Rae. Goal: Lyle 37.
Queen of the South: Scott, Paton, Jim Thomson, Lauchlan, McQuilken, Robertson (O'Neill 75), Burns, Scally, Moon, Dobbie (Weir 84), O'Connor (Henderson 89). Subs Not Used: Corr, Sloan.
Booked: Robertson, Burns. Goal: O'Connor 45.
Ref: C Allan