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Darren Lyon lashed in a surprise opener for Accies with a superb 25-yarder.
But the visitors left the impressive Mark O'Hara unmarked to side-foot home Danny Williams' corner minutes later.
Darian MacKinnon missed a sitter on the resumption for Accies, but Rory Loy, Yordi Tejsse and Danny Williams all missed chances to win it for Dundee.
The visitors might have snatched victory in the final moments but Michael Devlin's header was cleared off the line.
Dundee, having played a game more, are level at the top with Rangers - who host Motherwell on Saturday - and St Johnstone, who face Celtic in Saturday's early kick-off.
The hosts dominated in the first half but couldn't find a second goal and it was the same story after the break as they were unable to make their chances tell.
Hamilton got off to a great start when right-back Lyon sent  a stunning drive past Dundee keeper Scott Bain into the top corner.
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It was his first for the club and the 21-year-old will do well to top that strike, however long he plays the game.
But Accies were unable to build on it. Manager Martin Canning said prior to kick-off he hopes to complete the signing of former Partick Thistle defender Dan Seaborne over the weekend and you could see why he was so anxious.
Four minutes later, atrocious defending at a corner left O'Hara in acres of space to level with his second goal in six days.
The former Kilmarnock youngster, switched from defence to a more advanced midfield role by Dundee boss Paul Hartley, also scored against Rangers last weekend and impressed again here.
Faissal El Bakhtaoui, on his first league start for Dundee, showed enough flashes with his touch and link-up play to suggest the former Dunfermline striker can make the step up from League One.
Hamilton were nearly undone at another set piece after 38 minutes when Darren O'Dea steered his header from a Williams free-kick just wide of the target.
But whatever Canning said to his players during the interval certainly seemed to have a positive impact.
The visitors were much more impressive going forward in the second half with Louis Longridge causing problems down the left flank.
Unfortunately for Accies the end product wasn't clinical enough when they got within range of the Dundee goal, never more so than in the 49th minute after a great bit of link-up play through the middle.
Alex D'Acol fed in Darian MacKinnon behind the home backline but with only the goalkeeper to beat, the midfielder slid the ball agonisingly wide of the target from just eight yards.
Dundee were a shadow of the team that had dominated before the break but they still had a couple of decent chances of their own to win the game.
Loy forced Reni Matthews into a brilliant reaction save before substitute Teisse headed well wide from another Williams corner.
But it was Hamilton who came closest to winning it as Devlin's header was hacked off the line by Kevin Holt to make sure the home side secured a point.
Dundee boss Paul Hartley: "I'm not happy. We were alright for the first 15 minutes but not after that and we were lucky to get away with a point.
"In the second half, we just didn't perform at all.  We didn't pass the ball quick enough, create enough angles and played too many long balls. It is not acceptable.
"We're missing three key players in an attacking sense and we only had six on the bench. But we can't keep going on about Greg Stewart and Kane Hemmings leaving. They are gone.  Everyone else has to take responsibility now."
Hamilton boss Martin Canning: "I think we created enough opportunities to win it but for the second week in a row we didn't take the points we deserved from the game.
"It's really frustrating. On performance we should be sitting on seven points and be top of the league. Instead we only have two points and we have to start taking the opportunities we are creating.
"Our squad is strong and we are getting Dan Seaborne in to add some experience in defence while Rikesh Bingham offers something different up front - he's quicker and more mobile."
Match ends, Dundee 1, Hamilton Academical 1.
Second Half ends, Dundee 1, Hamilton Academical 1.
Foul by Dougie Imrie (Hamilton Academical).
Mark O'Hara (Dundee) wins a free kick in the attacking half.
Attempt saved. Ali Crawford (Hamilton Academical) right footed shot from the left side of the box is saved in the top centre of the goal.
Corner,  Hamilton Academical. Conceded by Mark O'Hara.
Substitution, Hamilton Academical. Greg Docherty replaces Massimo Donati.
Rory Loy (Dundee) wins a free kick in the attacking half.
Foul by Georgios Sarris (Hamilton Academical).
Attempt missed. Massimo Donati (Hamilton Academical) header from the centre of the box is close, but misses to the right.
Corner,  Hamilton Academical. Conceded by Julen Etxabeguren Leanizbarrutia.
Foul by Yordi Teijsse (Dundee).
Michael Devlin (Hamilton Academical) wins a free kick in the attacking half.
Corner,  Hamilton Academical. Conceded by Julen Etxabeguren Leanizbarrutia.
Substitution, Hamilton Academical. Gramoz Kurtaj replaces Louis Longridge.
Attempt saved. Louis Longridge (Hamilton Academical) right footed shot from outside the box is saved in the top centre of the goal.
Darren O'Dea (Dundee) wins a free kick in the attacking half.
Foul by Eamonn Brophy (Hamilton Academical).
Substitution, Hamilton Academical. Eamonn Brophy replaces Alejandro D'Acol.
Massimo Donati (Hamilton Academical) is shown the yellow card for a bad foul.
Yordi Teijsse (Dundee) wins a free kick in the attacking half.
Foul by Massimo Donati (Hamilton Academical).
Rory Loy (Dundee) wins a free kick in the attacking half.
Foul by Massimo Donati (Hamilton Academical).
Attempt missed. Danny Williams (Dundee) right footed shot from the right side of the six yard box misses to the left.
Corner,  Dundee. Conceded by Darian MacKinnon.
Substitution, Dundee. Yordi Teijsse replaces James Vincent.
Darren Lyon (Hamilton Academical) is shown the yellow card for a bad foul.
Foul by Alejandro D'Acol (Hamilton Academical).
Julen Etxabeguren Leanizbarrutia (Dundee) wins a free kick in the attacking half.
Attempt saved. Louis Longridge (Hamilton Academical) left footed shot from the left side of the box is saved in the top centre of the goal.
Louis Longridge (Hamilton Academical) wins a free kick in the attacking half.
Foul by Mark O'Hara (Dundee).
Foul by Massimo Donati (Hamilton Academical).
Rory Loy (Dundee) wins a free kick in the defensive half.
Attempt saved. Cameron Kerr (Dundee) right footed shot from outside the box is saved in the top centre of the goal.
Corner,  Dundee. Conceded by Michael Devlin.
Corner,  Dundee. Conceded by Michael Devlin.
Attempt missed. Dougie Imrie (Hamilton Academical) left footed shot from outside the box misses to the right.
Dougie Imrie (Hamilton Academical) wins a free kick in the defensive half.
Dundee moved joint top of the Scottish Premiership table but missed a chance to go two points clear as they were held at home by Hamilton.