The visitors started brightly and Scott Brown fired just past the post from 20 yards with six minutes played and moments later Kevin Nichol fired high over the crossbar from a similar range.
Midway through the half a brilliant tackle by Gary Caldwell by Hibs denied Stephen Milne what looked like the opening goal, the Hibs defender taking the ball away from Milne just as he was about to shoot from six yards.
The home team went ahead with 38 minutes played. Steve Lovell broke clear on the right and with Milne screaming for a pass inside, Lovell decided to go for goal himself and from the right side of the box fired low into Daniel Anderson's right-hand corner.
The visitors drew level on the stroke of half time when Derek Riordan collected a pass from Tom McManus and sent a low right foot shot past Julian Speroni from 12 yards.
The visitors were then awarded two penalty kicks in a two-minute spell early in the second half. The first one looked soft when Gary Caldwell went down in a challenge with Brent Sancho and the second was for a trip on Tom McManus by Sebastian Kneissl.
Derek Riordan took both kicks and made no mistake with his first on 50 minutes but was denied a seven minute hat-trick when Speroni dived to his left to save the striker's second on 52 minutes.
Hibs scorer Riordan had two attempts at goal in quick succession with the first being easily saved and the second going wide of the target with 20 minutes remaining as he went in search of his third goal.
Dundee grabbed a deserved equaliser as the match drifted into time added on.
A good break down the right by Nacho Novo saw the Spanish striker charge into the danger area and play a good ball back across goal to Milne who forced the ball home from four yards to give his team a share of the points.