After a quiet opening spell the visitors created three good openings in a two minute period when Brian Carrigan and then Paul McMullan both shot just wide of the target before Derek Soutar did well to block John Robertson's close-range header.
Carrigan should have put Hamilton in front four minutes before the break but when Soutar parried the ball straight to him four yards out the Accies striker blazed his shot high over the bar.
Simon Lynch fired the home team's first goal attempt wide of the target on the stroke of half-time.
Dundee substitute Gavin Swankie missed the target from close range and then Callum McDonald saw his header cleared off the line both from Garry Brady corners early in the second half.
With 72 minutes played the visitors took the lead when Patrick Keogh latched on to a through ball from Carrigan and poked the ball past the onrushing Soutar from 15 yards.
Dundee grabbed the equaliser three minutes from time when the Hamilton defence failed to clear their lines and Steven Craig bundled the ball home from close range.