Dundee earned a draw at Easter Road but lost ground in their Scottish Premier League relegation battle because of Ross County's win at St Mirren.
John Baird rounded off a great move with a left-foot shot in eight minutes to put them in front against Hibernian.
The home side pushed hard after the interval and Leigh Griffiths curled in a sweet free-kick to level the score.
Hibs then had the upper hand but they had to rely on Ben Williams to save from Steven Milne and Colin Nish.
Having completed their Scottish Premier League winter break, Dundee resumed their battle to stay in the top tier knowing that second-bottom County had moved 12 clear of them with a convincing win against St Mirren at lunchtime.
Perhaps it was the scale of that gap that spurred the Dark Blues on at Easter Road.
Baird put them in front, his composed shot finishing off an excellent move involving defender Brian Easton, Mark Stewart and striker Nish, back at one of his former clubs.
Tim Clancy headed over from a corner and Jorge Claros clipped a shot over the bar as Hibs looked for a swift reply.
But the home side had goalkeeper Williams to thank in 18 minutes when he raced off his line to save at the feet of Milne seven yards out, after he had played a neat one-two with Nish.
Lewis Stevenson cushioned a looping cross from the right with a delightful lay-off into the path of Eoin Doyle, but the striker's shot was powder puff and Rab Douglas in the Dundee goal mopped up with ease.
Nish went close to making it 2-0 with a left-footed chip that had Williams scampering to his far post and at the other end David Wotherspoon sent a header at Douglas's goal, corkscrewing his body to direct the ball a foot over the bar.
Baird looked impressive when he got on the ball and when he found space in the Hibs box and cut the ball back, attacking midfielder Stewart should at least have hit the target instead of blazing over the bar.
Doyle hit the target again with a first-time curling shot but once more the Hibs forward's effort lacked power and Douglas made the easiest of saves from the Irishman.
Hibs won two corners in the opening minute of the second period, no doubt stung by the booing at half-time by their fans.
Those failed to produce a goal; that responsibility fell three minutes later to Griffiths who whipped a free-kick over the Dundee wall and left Douglas diving despairingly to his left as the ball flew in at the near post.
When Griffiths tugged a 20-yard shot a few feet wide moments later it looked like Hibs would go on to take all three points.
But it was Dundee who had two excellent chances to get in front. A free-kick was headed into the six-yard box where Milne fired a shot in at the near post and Williams made the smartest of blocks.
The Hibs keeper came to the rescue again when Easton's marauding run from the halfway line set up Nish whose attempted dink past the goalie was thwarted by Williams' positioning and quick reactions.
Neither side could find the winner thereafter and, while both teams will have left the pitch frustrated, a draw was the right result.