Hamilton player-boss Martin Canning had put the visitors ahead three minutes earlier but the Accies could not hold on and had to settle for a point, although at least they ended a run of four defeats in a row.
Hamilton began really brightly and Tony Andreu was within inches of giving them a first-minute lead after receiving from Ali Crawford but Scott Bain did well to push the midfielder’s shot onto the post, before Canning had a downward header from a corner kicked off the Dundee line.
Jason Scotland was then hauled down by Kostadin Gadzhalov and Dundee’s Bulgarian defender was possibly fortunate to escape with just a yellow card, Jesus Garcia Tena putting the subsequent free-kick straight into the wall.
Dundee then began to up their game and Gadzhalov’s near post header at a corner was pushed away by Michael McGowan.
And the hosts felt they should have had a penalty for handball against Garcia Tena but the referee waved away their appeals.
However, Hamilton finished the half on the front foot and the ball hit Canning from a corner and bounced over the bar before Scotland should have done better than shoot too high after he had powered into the penalty area.
Dundee manager Paul Hartley was clearly unimpressed by his team’s first-half efforts and he brought on Luka Tankulic and Stephen McGinn at half-time.
But it was the Accies who went close again after the interval as Scotland found himself clean through on goal, only to be foiled by Bain, who raced off his line to rescue the hosts.
And Hamilton then foolishly hampered their own efforts as Dougie Imrie was shown a straight red card for an off-the-ball stamp on Greg Stewart.
Suitably encouraged, Dundee pressed forward and Stewart’s deflected low shot was only just wide of the post.
Stewart then tried his luck again from long-range and his powerful shot was only just too high before defender James McPake headed for goal from a corner, only for McGovern to save.
And it was Hamilton who then went in front when Canning rose to meet a Crawford corner at the back post and powered a header past the defender on the line and into the net.
However, Stewart had been on a one-man mission for Dundee in the second half and he earned them a share of the spoils with a wonderful goal, cutting inside and then curling a shot into the top corner of the net from the edge of the area.