Only some excellent goalkeeping from Kyle Letheren kept the visitors at bay, but Hamilton will regret a string of missed opportunities.
The Dundee stopper was called into action early on to keep out a Darian MacKinnon shot after the Hamilton player had fashioned an opening for himself with some excellent play.
From the resultant corner, Letheren had again to prove his agility to touch a James Keatings' header against the face of his crossbar.
There was a chorus of disapproval from the home fans at half-time after watching their side play second fiddle and it did not improve much after the interval.
Mickael Antoine-Curier, a former favourite at Dens Park, was quickly at the forefront of another Accies attack, but Letheren again showed his worth to keep the league leaders at bay.
Remarkably, Dundee could have nicked all three points had Gary Irvine shown a bit more composure in front of goal deep into the second half, but he skied his effort to ensure both sides went home with a point apiece.
Falkirk and Alloa Athletic failed to make any ground on the leaders as they both suffered defeats.
Falkirk lost 1-0 to a late strike from Greg Stewart at Cowdenbeath in a disappointing match.
The visitors had the better of the first half and Kieran Duffie miscued in front of goal midway through the half when he had a clear chance to score.
Jay Fulton also went close on a couple of occasions, but the hosts proved resilient and, as the match wore on, looked increasingly likely to gather the three points.
Kane Hemmings was denied by Michael McGovern before Stewart showed impeccable timing to net the winning goal with just a minute left.
Dumbarton ruined Alloa's unbeaten home league record as they carved out a fine 2-1 win at Recreation Park.
Ian Murray's side had a couple of chances before Andy Graham put them ahead in the final minute of the first half, after being given too much time to control the ball in the Alloa penalty area.
Stephen Simmons equalised nine minutes into the second half when Dumbarton failed to deal with a corner and the midfield player had time to pick his spot.
Scott Agnew, though, put Dumbarton back in front with a 71st-minute penalty after Graham was fouled and Dumbarton held on for the win.
John McGlynn's first match in charge of Livingston saw Morton come back from 2-0 down to claim a 2-2 draw.
Club captain Simon Mensing put the West Lothian side ahead after four minutes with a powerful header from Martin Scott's corner before Marc McNulty made it 2-0 shortly afterwards.
Reece Hands fired home from 25 yards to bring the Greenock side back into the game on 34 minutes and Kabba Cham then levelled the scores seconds before half-time.
Dougie Imrie almost gave Morton an unlikely victory, striking a post midway through the second half.
Elsewhere, Greig Spence's 17th-minute goal was enough to give Raith Rovers a 1-0 win at Queen of the South, who had Mark Durnan sent off 12 minutes from time for aiming a kick at the goalscorer.