The in-form 25-year-old linked up brilliantly with the returning Anthony Stokes to volley home the decisive strike in the second half after Marcus Haber had cancelled out Martin Boyle’s quick-fire opener.
The buoyant Hibees are just two points adrift of second-placed Aberdeen after the Dons could only draw at Hamilton. Dundee, meanwhile, have now succumbed to five defeats in a row.
However, they were far from outclassed in the capital and, if not for a truly wonderful save from Ofir Marciano when the encounter was tantalisingly balanced at 1-1, it could have been a very different afternoon.
The visitors made five changes to the side dismally defeated 3-1 by Hamilton last weekend, with Roarie Deacon, Faissal El Bakhtaoui, Kevin Holt and Cammy Kerr coming into the side.
The most notable alteration, however, was Elliot Parish replacing Scott Fox between the sticks amid suggestions of a bust-up between the Dens Park number one and manager, Neil McCann.
With all eyes on Parish in his first outing for the Dee since joining from Accrington in the summer, he was picking the ball out of the net after 63 seconds.
Boyle robbed Lewis Spence before skipping past a weak challenge from Holt and unleashing a ferocious low drive into the bottom corner.
However, the Taysiders belied a nightmare start and their run defeats to restore parity after 21 minutes.
The excellent Deacon danced past Lewis Stevenson on the wing and delivered a fine cross for Haber to nod beyond Marciano.
Dundee defender Jack Hendry then headed just wide of the post as McCann’s men ended the half in the ascendancy.
Things went from bad to worse for Hibs when Dylan McGeouch had to be replaced by Stokes after falling to the turf clutching his hamstring. It is another setback for the luckless playmaker, who has been in scintillating form of last after seeming to have beaten his fitness woes.
David Gray and Brandon Barker were replaced by Ryan Porteous and Vykintas Slivka at the break as Lennon rung the changes.
But it was more of the same as Dundee almost claimed the lead with El Bakhtoui forcing Marciano into a stunning low save with a drive from just inside the box.
Hibs took full advantage of that reprieve when Stokes picked out Murray with a superb delivery, allowing the in-form striker to volley home his 13th goal of the campaign in comprehensive style.