Commons gave the home side the lead only for Niall McGinn to equalise in first-half stoppage-time, but second-half injury-time goals from Derk Boerrigter and Commons saw Celtic take all three points.
Celtic dominated the early possession but it was the away side who had the first on shot target through Michael Hector whose long-range effort failed to trouble Fraser Forster.
The home side hit back with an eleventh minute Darnell Fisher shot, saved by Jamie Langfield as Celtic began to assert their superiority
Georgios Samaras and Teemu Pukki both summoned Langfield into action moments later but the Aberdeen goalkeeper stood firm, saving shots from both players.
Aberdeen looked like they were weathering the storm and McGinn had a chance to give them an unexpected lead but his header failed to trouble Forster.
But their resilience didn't last long as Celtic managed to break the deadlock after 35 minutes - Commons picked up the ball near the edge of the area and rifled home right-footed into the bottom right corner to give the home side a deserved lead.
With the half drawing to a close Russell Anderson had a gilt-edged opportunity to get Aberdeen on level terms but his close-range header was over the bar.
The away side looked like they would be trailing going into the break but they snared an equaliser in first-half injury-time.
Emilio Izaguirre conceded a corner and Calvin Zola smuggled the ball to McGinn who bundled the ball home from close-range.
Celtic began the second half positively forcing a succession of early corners. Charlie Mulgrew then had a couple of shots for the home side but was unable to trouble Langfield.
Samaras thought he had given Celtic a 62nd minute lead after latching onto a pass from Commons but his flick rebounded off the post. Minutes later, Langfield denied Commons as Celtic tried to reinstate their lead.
McGinn almost stole an unlikely victory with three minutes left to play but his left-footed effort came back off the post with Forster beaten.
There was more drama to come however. Celtic took an injury-time lead through Boerrigter who bundled the ball home from a corner.
And the home side sealed the three points when Commons found himself unmarked to the right of the six-yard box before calmly slotting home as Celtic maintained their five-point lead at the top of the Scottish Premiership.