Stefan Scepovic found the back of the net on his debut a few minutes later, but the Serbian's first goal for his new club was ruled out for offside.
Commons had several chances to extend the home side's advantage before the break, but was frustrated by the Aberdeen defenders.
Celtic added a second just moments into the second half as Commons slotted the ball in from a Callum McGregor ball into the box.
The visitors did pull one back on the hour mark when a ball to the back post was headed in by David Goodwillie, getting Aberdeen back into the tie.
Willo Flood tried to force an equaliser, but Gordon punched it clear before Goodwillie was flagged offside while trying to add his second.
McGregor and John Guidetti both had chances to put the win beyond doubt in the final minutes, but the hosts did enough to hold on for all three points.