Iain Davidson gave Dundee the lead eight minutes from the break, but County hit back strongly and substitute Gary Glen fired home a deserved equaliser with 16 minutes remaining.
Both sides took time to settle and it took until the 15th minute for the first real effort on goal. County's Alex Cooper, who was making his second start of the season, got behind the Dundee defence and his cross into the box was knocked back by Colin McMenamin for Mark Fotheringham, whose low drive flew wide of the upright.
