Celtic lead Dundee 1-0 thanks to Anthony Stokes's goal on the stroke of half time.
Dundee nearly took the lead within the opening 60 seconds when a ball from the right found Greg Stewart unmarked inside the Celtic penalty area, but the striker fired wastefully over the bar.
Paul Hartley's side gave the hosts another scare on five minutes when David Clarkson's lob deflected off Craig Gordon before being cleared off the line.
Celtic carved out their first chance of the game when Stokes fired in a corner which was met at the near post by Kris Commons, but the midfielder sent his header narrowly wide.
Goalkeeper Scott Bain was off his line sharply to deny John Guidetti just before the half-hour mark, before Gary Irvine volleyed over for the visitors.
Just as it appeared Dundee would be going in level at the break, Stokes rose highest to head home a Commons corner to give Celtic the lead.