Scorers: Dundee - Stewart (3), McGinn (43), MacDonald (59), Boyle (70)
Paul Hartley’s side prevailed with plenty to spare courtesy of first-half goals from Greg Stewart and Paul McGinn before further strikes after the break from Peter MacDonald and Martin Boyle secured the win against their lower league opponents.
It was hard on Grant Murray’s visitors who struggled to cope with their slick top-flight opponents who duly stretched their unbeaten run.
Dundee made six changes from the side which secured their first Premiership win away to St Mirren the previous weekend. Keeper Scott Bain, Iain Davidson, Peter MacDonald, Phil Roberts, Greg Stewart and Martin Boyle all came in from the start, while Rovers had ex-Dark Blues pair Ryan Conroy and Christian Nade in their line-up.
The hosts had beaten League One outfit Peterhead 4-0 in the previous round but were expecting a tougher test from their Championship visitors who were bidding to bounce back from their 4-0 league defeat by Hearts a few days earlier.
But Dundee powered ahead as early as the third minute.
MacDonald nodded the ball on to Boyle whose shot was deflected wide for a corner.
From the resultant set-piece, Roberts’ curled corner was met by Greg Stewart who rose unchallenged inside the six-yard box to bullet a free header past visiting keeper Kevin Cuthbert.
That helped ease any nerves the home team might have been feeling but in 12 minutes they breathed a huge sigh of relief.
Raith picked up a free-kick 22 yards from goal and up stepped set-piece specialist Conroy to try his luck.
The former Dens midfielder curled an effort over the Dundee defensive wall with his trusted left foot, only to see Bain scurry across his line to get an outstretched arm to palm his attempt over the bar at the expense of a corner.
Then, in 19 minutes, Raith threatened again as Conroy picked out Martin Scott who, in turn, found Mark Stewart whose low left-foot shot fizzed just past Bain’s far post.
At the other end, Stewart came within inches of grabbing his second of the night as he latched on to Boyle’s lay-off, only to see his angled shot from outside the penalty area fly narrowly over Cuthbert’s bar.
Nade then had a mazy run followed by a shot which was saved by Bain as the Fifers refused to let their top-flight opponents have it all their own way, before Stewart did something similar for Dundee which brought out a decent save from Cuthbert.
But the hosts weren’t to be denied as Paul McGinn made it 2-0 two minutes before the interval, picking up possession and cutting inside on to his left-foot to send an unstoppable 25-yard shot high into the top corner past the helpless Cuthbert.
Dundee brought on striker Paul McGowan for defender Thomas Konrad after the break and wasted no time in going for a killer third goal.
McGinn linked with MacDonald whose knock-down was met by McGowan, but his ambitious volley was comfortably held by Cuthbert.
The home team had a goal disallowed in 52 minutes when Boyle was judged to have kicked the ball out of Cuthbert’s hands from point-blank range.
However, they succeeded in putting the tie beyond any doubt with a well-worked third goal in 59 minutes.
Stewart sent Boyle racing clear down the right and his inch-perfect cross was swept home by MacDonald from close-range for his second goal in as many games.
Then, in 70 minutes, Boyle slotted home from a few yards to seal matters after MacDonald’s shot had been blocked.
Dundee: Bain, Irvine, Konrad (McGowan 46) McPake, Davidson, MacDonald (Tankulic 60) Roberts, G Stewart, McGinn, McAlister (Harkins 67) Boyle.
Raith Rovers: Cuthbert, Thomson, Perry (Ellis 84) Watson, Moon (Callachan 77) M Stewart, Scott, Conroy, Vaughan, McKeown, Nade (Anderson 57).
Referee: K Clancy