Despite the narrow scoreline Hibs could have won by more, Kevin Nisbet and Jamie Murphy both going close in the second half.
Paul Hanlon and Paul McGinn were brought back into the starting line-up after serving their suspensions while Jake Doyle-Hayes returned after illness.
The first half-hour was short on highlights for either team, with Hibs losing Chris Cadden to injury 20 minutes in and no clear-cut chances.
On 34 minutes, the game stuttered into life as Martin Boyle’s mazy run from just inside his own half and subsequent cross was superbly headed past Adam Legzdins – by Dundee’s Paul McMullan. It was a harsh blow for the winger, who had done well to make up the yards back to his own penalty area, but a lead that Hibs probably just about deserved, having had the better of the half-chances before that point.
Nisbet nearly made it two just before the interval. The through-ball from Christian Doidge, who had replaced the stricken Cadden, was inch-perfect but although his strike-partner danced the ball past Legzdins, former Easter Road favourite Liam Fontaine was on hand to block the chipped effort.
The visitors emerged the livelier of the two teams after the break and after Jake Doyle-Hayes miscued a clearance just in front of his own six-yard box, the ball sat up nicely for Danny Mullen but his effort cleared the bar by some distance.
Hibs continued to probe and Lewis Stevenson had a low shot knocked behind for a corner before the veteran defender incurred the wrath of Matt Macey as he cleared for a corner with the goalkeeper waiting to collect the ball.
On the hour mark Hibs could, and arugably should, have doubled their advantage. Joe Newell did well on the left flank to keep the ball and as he swung the ball in low and hard towards the onrushing Nisbet a goal looked a certainty. However, the Scotland internationalist skied his effort from close range.
Ten minutes later Murphy, on for Nisbet who had twice gone down with an injury, passed up a glorious chance to give Hibs breathing space. Boyle scampered onto a loose ball and headed for the byline, picking out the substitute with a perfectly weighted ball but Murphy took a touch, allowing Legzdins to set himself and block the forward’s attempt from close range.
Josh Campbell wasn’t too far away with an ambitious effort from distance as the game approached the final ten minutes but the encounter more or less petered out, with Macey coming for a high ball in injury time as the Dark Blues sought a late leveller.
It was by no means a vintage performance from Hibs, but a rare clean sheet – and a league win – will be a welcome change for the Capital club ahead of Sunday’s Premier Sports Cup final against Celtic.
If this is to be the last game for interim boss David Gray, he leaves with an unbeaten record; the necessary steadying of the ship before the arrival of the next permanent manager.