A Peter Grant goal was enough to give Morton the points and end a run of three losses at Cappielow.
David Hopkin’s men were second best for long spells of the first half but went into the interval in front. That was mainly down to the wastefulness of Dundee who spurned a couple of clear-cut opportunities, Danny Rogers’ terrific save from Paul McGowan perhaps the biggest chance of the lot.
McGowan set up a chance for Declan McDaid, with the winger’s shot deflected wide. Jordan McGhee was also guilty of spurning a big chance from a McDaid corner, steering a free header wide.
Grant didn’t make the same mistake when Nicky Cadden found him from a free-kick on the stroke of half-time. Grant met the cross and thumped the ball past Jack Hamilton.
Dundee sent on Andrew Nelson and new recruit Graham Dorrans to add some firepower but there was little late threat from the Dens Park side. Indeed, Morton should have added to their tally as both Reece Lyon and John Sutton went close.