The in-form Hoops midfielder drove past Caley keeper Dean Brill after two minutes for his 15th goal of the season but the Hoops failed to capitalise on that in the first half as the home side grew in confidence.
Commons saw a chip shot clip the bar after the break but although the visitors could not find top gear, they did enough to stretch their unbeaten run in the league to 18 games.
Caley made life difficult for themselves by going behind so early in the game but boss John Hughes will take some satisfaction in the way his side responded.
In what was a freezing day in the Highlands, the visitors showed one change to their line-up.
Winger James Forrest came in for Darnell Fisher who dropped out of the squad altogether, with Adam Matthews moving back to right-back.
Hughes kept the same starting XI which fought out a goalless draw with Partick Thistle at Firhill on Boxing Day, with 17-goal Billy McKay leading the line.
However, it was Celtic's top scorer, Commons, who got the Hoops off to a great start.
After the Caley defence failed to clear their lines, the former Nottingham Forest and Derby player played a smart one-two with Georgios Samaras before drilling the ball low past Brill and into the far corner of the net.
The home side were stunned at the early set-back but slowly worked themselves back into the game.
In the 11th minute midfielder Aaron Doran tested Hoops keeper Fraser Forster with shot from distance after finding a pocket of space in front of the Celtic penalty area.
Danny Williams then had an effort from distance minutes later which went well wide of the target but it revealed a growing confidence among the home side.
However, in the 31st minute Celtic had a decent chance when left-back Emilio Izaguirre's cross from the left ended up at the feet of Anthony Stokes, via the head of Caley midfielder Ross Draper.
The Republic of Ireland striker pulled his shot back across goal and wide of the target.
The rest of the half was evenly-matched - with Samaras booked after a foul from behind on Draper - but Caley were far from knocking at the Parkhead door.
With three minutes of the opening 45 remaining, Hoops midfielder Joe Ledley put his side in trouble when he was unnecessarily dispossessed in the corner by Marley Watkins.
When the ball went to Graeme Shinnie, the Caley skipper powered in a drive which Forster did well to beat away, with Celtic surviving an intense but brief spell of pressure.
The home side came out energised for the start of the second-half and four minutes in Shinnie took the ball from Samaras and fired in another powerful drive which Forster parried away for a corner, again defended by the visitors.
Celtic were struggling to lift their game but just before the hour-mark Commons got on the end of a good cross from Stokes and flicked the ball inches wide of the far post.
Minutes later, a wonderful turn and chip from inside the Caley box by the Hoops midfielder saw the ball clip the bar before going over, another signal that the champions were coming back into the match.
A fine, flowing move by Celtic in the 68th minute saw Commons fire in another drive, this time from 10 yards, but this time Brill made the save, before skipper Scott Brown fired wide.
In the 75th minute, as Caley enjoyed a spell of pressure, Forster made another save, this time from Doran's 25-yard drive, before tipping a Gary Warren header over the bar.
However, there was to be no late rally from the home side and indeed Brill was forced into a save from Brown with two minutes remaining, although Draper missed a good headed chance with seconds remaining.