Commons converted a first-half penalty after Kieran Tierney was fouled in the box, before firing an unstoppable shot into the far corner of the net after his corner was only half-cleared in the second half.
Leigh Griffiths had given Celtic the lead after latching onto the end of a Scott Brown pass to fire past Luis Zwick. Dedryck Boyata then grabbed the second goal, heading home an inviting Scott Armstrong cross.
Commons added the penalty just before the break, before Gary Mackay-Steven almost added a fourth straight after the restart, his low strike being turned onto the post by Zwick.
Celtic continued to push forward with Mackay-Steven continually testing Zwick in net, but it was Brown who grabbed the fifth after driving to the byline and hammering in a shot off Aaron Kuhl.
The league leaders now go four points clear at the top, while Dundee are languishing far behind with just five points.