Despite boasting two thirds of possession and weighing in with 26 shots, seven of which were on target, the Hoops could not breach their opponents' rearguard.
The hosts ramped up the pressure from the off, but the best chance of the opening 20 minutes came from Dundee as Simon Murray forced the returning Craig Gordon into a fine save.
On the stroke of half time, a tackle by Boyata on Roarie Deacon sent the ball off the post, almost giving Dundee the lead with an own goal, though ex-Dees man Jack Hendry was then able to clear.
The second half saw the Bhoys step up their attacks as Odsonne Edouard and Hendry threatened, but the league leaders could still not find a breakthrough come the final whistle.
Dundee, meanwhile, move five points clear of the relegation zone.
CELTIC (4-2-3-1): Gordon; Lustig, Hendry, Boyata, McGregor; Brown, Armstrong; Forrest, Rogic (Ntcham 66'), Sinclair (Edouard 66'); Dembele (Griffiths 65')
DUNDEE (3-5-1-1): Parish; Caulker, Kusunga, Meekings; O'Hara, Kamara, McGowan (Wighton 87'), Spence, Holt; Deacon (Moussa 66'); Murray (Leitch-Smith 77')