Mikael Lustig set up the opening goal for the visitors just six minutes into the tie, crossing in for Leigh Griffiths to head in at the near post.

Kris Commons tried to make it two for the Scottish champions a few minutes later, but Stefan Johansen lost the ball before he could turn the through ball in.

Scott Brown and James Forrest both missed chances from the edge of the box as the captain had his effort saved before the latter fired wide.

Craig Gordon was called into action just before the break to keep Celtic ahead, palming a Paul McGowan effort clear for the visitors.

Ronny Deila's side doubled their lead just moments after the restart as Johansen blasted the ball in after Griffiths had his header saved.

Johansen had a chance to add his second on the hour mark as he curled the ball in from the outside of the box, but Scott Bain tipped the ball onto his crossbar.

Griffiths continued to stretch the Dundee defenders as he also pushed for his second of the afternoon, but he put his finish wide after rounding a couple of defenders on the edge of the box.

Anthony Stokes could have made it three for the Hoops as the final 15 minutes approached, but he hit it just over as he struck on the turn.

McGowan continued to look the most likely source of a goal for the hosts, but Jason Denayer was back on the line to spare Gordon after the striker had rounded the keeper.

John Guidetti came on late on to try to end any hopes of a Dundee comeback, but he could not find the back of the net with a couple of half-chances.