Eoin Doyle headed the home side into a first-half lead before Leigh Griffiths gave Hibs a comfortable advantage with an early second half penalty. David Wotherspoon completed the scoring with a calm finish 16 minutes from time.
The hosts had endured some lucky escapes in defence when the game was still in the balance, but overall they secured a well-earned three points.
Pat Fenlon made only one change from the team that lost 2-1 to Aberdeen last weekend. Half-time substitute Ryan McGivern did enough to impress despite the loss and he was preferred to Alan Maybury in the left-back role.
Davide Grassi's return to fitness ahead of schedule gave the visitors a boost as he slotted straight into the starting XI alongside Kyle Benedictus, who was preferred to Matt Lockwood at centre-back.
Passive play from one half of that partnership almost had the visitors a goal down in 10 minutes. Benedictus' poor header fell to Griffiths, in space, 30 yards from goal. The striker advanced before firing a low shot that rippled the side netting.
Dundee scored early when they won at Tynecastle earlier in the season and would have done so at Easter Road but for a spectacular save from Ben Williams. Jim McAlister's drilled left-footed shot from inside the penalty area seemed destined for the bottom corner, but Williams somehow got down in time to push the ball away.
Following the resultant corner Hibs went straight down the other end where Doyle saw his header from inside the box comfortably held by Rab Douglas, but there was nothing the veteran stopper could do when the Irishman was presented with a similar chance on 28 minutes.
Paul Cairney was the architect. Running in between the attentions of Ryan Conroy and Gary Irvine, the midfielder won the race to the byline and his cut-back cross found Doyle rising highest in the six yard box. The striker headed past Douglas for his fourth goal of the season.
Colin Nish, returning to his former home ground, should have restored parity five minutes before the half. The striker got in front of James McPake to receive Iain Davidson's cut-back, but an off-balance Nish could only side-foot his effort wide of goal. McAlister then failed to test Williams when he sliced his shot from 12 yards.
Dundee were made to rue those missed chances five minutes after the restart.
Doyle's clever back-heel found David Wotherspoon inside the penalty area. The midfielder cut across goal looking for an angle but instead found teammate Cairney charging in. Before Cairney could take the shot he was bundled down by McAlister and referee Willie Collum showed no hesitation in pointing to the spot.
Griffiths stepped up and delivered a perfect penalty, striking the ball high and into the net off the inside of the post.
Having set-up both goals Cairney almost got himself on the score-sheet as he clipped the ball past a hesitant Douglas, but Gary Irvine blocked the shot on the goal-line.
Dundee rarely looked threatening and it was Hibs who were always likelier to add to the score-line. On 70 minutes Griffiths low shot from 30 yards had to be saved by a diving Douglas. The keeper was called into action again two minutes later, parrying the striker's fiercely struck effort from the right of the penalty area.
On 74 minutes Hibs had their third. A nice through ball from Jorge Claros was gathered by Wotherspoon on the right. The Scottish under-21 internationalist moved into the penalty area, feinted a shot with his right foot, rolled the ball back onto his left and passed the ball into the far corner of the net.