Early goals in either half from former Dundee striker Leigh Griffiths and midfielder Stefan Johansen set Ronny Deila’s side up for victory.
Celtic struck with just seven minutes on the clock as Nir Bitton found Mikael Lustig with a clever pass and the right-back whipped a quick delivery into the box for Griffiths to find the far corner with a glancing header at the front post.
James McPake came to his team’s rescue to intercept a ball from Johansen inside the penalty area, and the Dundee defender deflected a Scott Brown effort from 25 yards wide of the post shortly after that.
The visitors came close again when James Forrest robbed Gary Irvine just inside the Celtic half and raced on to a return pass from Johansen, but his shot from 12 yards was blocked by Dundee ‘keeper Scott Bain.
Two minutes later Kostadin Gadzhalov hooked a volley from 20 yards a foot wide of the target after a spell of head-tennis at a Dundee corner.
At the other end, Griffiths took a pass from Kris Commons and beat McPake with a clever flick before dispatching a volley which Bain saved at his front post.
And a minute before the break, Bain again thwarted Celtic as Johansen robbed McPake inside the penalty area but his low drive was blocked by the ‘keeper’s legs.
Celtic then survived their biggest scare of the half when Jason Denayer took the ball off the toe of Paul McGowan on the edge of the box and Craig Gordon was forced into a diving save to stop the ball dropping inside his right post.
But the Hoops put the game beyond Dundee two minutes after the break when Lustig again picked out Griffiths with a cross as the striker drifted in at the far side of the box, and although Bain saved the downward header, Johansen pounced on the rebound to net from six yards.
Bairn later had to make an acrobatic save to keep out a Johansen delivery with the outside of his boot, as the ‘keeper touched the ball on to his back post.
Tony Stokes came off the bench at the interval to replace the injured Kris Commons, and the Irishman crashed a dipping shot over the bar from just outside the box.