After their historic 1-0 extra-time victory over Celtic in midweek, Ton had hoped to carry their momentum into the league trip at Dens Park.
Manager Allan Moore, whose brother, Steven, tragically died during the week, made the brave decision to travel with the team and take his place in the dugout.
And he would have been delighted with his side’s first half after they managed to pick up where they left off at Celtic Park, defending resolutely and taking the lead through a set-piece.
Tomas Peciar was a rock at the heart of the Ton defence against Neil Lennon’s men, in particular the way he won header after header as Celtic fired in a seemingly never ending stream of corners.
And the Slovak defender proved he could be just as dominant in the opposition box as he rose highest to power home Dougie Imrie’s inswinging corner on 23 minutes.
This was, however, the proverbial game of two halves in which the Ton defence took on the appearance of the pre-Celtic rearguard in the first five minutes after the break.
With just two minutes of the second half gone, Peter MacDonald flicked the ball past Nicolas Caraux from close range after pouncing on Declan Gallagher’s knockdown.
Former Ton frontman MacDonald then turned the match on its head a further two minutes on when he hooked Nicky Riley’s cross high into the roof of the net.
Ton looked to be running on empty after their midweek exertions and conceded a third on 70 minutes when ex-Scotland striker Craig Beattie fired in after the ball broke for him inside the box.
In truth, the visitors were fortunate not to concede more, with MacDonald passing up two glorious opportunities to complete his hat-trick, and left Dens a well-beaten side by full-time.
The defeat combined with Livingston’s 5-1 victory over Cowdenbeath leaves them propping up the table after seven matches.
Morton (4-2-3-1): Caraux; Taggart, Page, Peciar, Fitzpatrick; Habai (Stirling, 69), Bachirou; Wallace, Imrie ©, Fulton; Campbell (McNeil, 76).
Subs not used: McLaughlin, Knight, Verlaque, Gaston (gk).
Dundee (4-4-2): Letheren; Irvine, Gallagher, Davidson, Dyer; Riley (McBride, 88), McAlister, Rae ©, Conroy; Beattie (Monti, 73), MacDonald (Doris, 88).
Subs not used: Lockwood, McBride, Monti, Doris, Benedictus, Boyle, Twardzik (gk).
Referee: Iain Brines