The Scotland international fired a low drive from inside the box past Jack Hamilton just seconds before break, securing Hibs a 1-0 win.
That effort was enough to hand Jack Ross' side their second victory over the Dens Park side in the competition after Hibs won 4-1 in the last group game 13 days earlier.
Hibs were without Paul Hanlon after the defender failed to recover from a groin strain.
Dundee boss James McPake decided to make four changes to the team following last weekend's woeful league defeat at Ayr United. Goalkeeper Jack Hamilton was recalled, as were Alex Jakubiak and Jonathan Afolabi. Defender Liam Fontaine was also handed his first start against his former club.
Hibs made a bright start. A Stevie Mallan corner after only three minutes found Darren McGregor in the six-yard box but the ball hit the defender's leg and looped over.
Dundee were struggling for ideas in the final third although Charlie Adam's deliveries into the area posed questions of the Hibs rear-guard.
Hibs marksman Nisbet should have at least worked the goalkeeper with a shot from 12 yards that fizzed over after Martin Boyle's cross came back off the post.
But Nisbet played his part in the goal a minute before the interval.
The forward slipped in Murphy inside the area and the on-loan Rangers playmaker fired a left-footed shot past Hamilton from an angle inside the box.
Dundee thought they had levelled just minutes after the restart only to be disappointed by the linesman's offside flag.
Fontaine's long throw was flicked on by Lee Ashcroft and the ball came back off the bar. Jakubiak pounced on the rebound to score but was deemed offside.
Hibs sub Drey Wright brought out a save from Hamilton moments after coming on and should have done better with another effort he sliced well wide from 15 yards after being teed up by Doidge.