Ominously for the chasing pack, the leaders have won four on the trot in the league to open up a five-point gap, with a game in hand over most of their rivals.
Dundee were widely tipped to struggle after receiving a late invitation to the top table and have picked up just 12 points from their opening 18 matches.
Six points adrift of Ross County, Barry Smith's men have conceded 11 goals in their last four outings after signs of a revival in November.
Celtic boss Neil Lennon said: "It will be a cup final for them, but I suppose every game is for them really.
The bookies see nothing more than an away win though and Celtic are no bigger than 2/5 to win away!