However, the home fans have the Dons' calamity keeper Jamie Langfield to thank for the three points.
The Pittodrie side looked comfortable enough as the champions struggled until Langfield made an horrendous mess of Commons' shot from distance at his near post after the Hoops midfielder had played a short corner with Joe Ledley.
Langfield, nicknamed Clangers, will not want to see his aberration again but Celtic will certainly have to do better in Finland on Wednesday night if they are to build on their 2-1 first-leg lead against HJK Helsinki in their Champions League third qualifying round tie.
It was a lacklustre display by Celtic, although goalkeeper Fraser Forster had little to do.
Celtic legend Sean Fallon, the 90-year-old former player and assistant manager, unfurled the championship flag before kick-off along with Hoops chairman Ian Bankier but after that it all went flat.
Celtic skipper Scott Brown and James Forrest failed fitness tests and with defender Charlie Mulgrew suspended after being sent off in a pre-season game against Ajax, manager Neil Lennon was forced to reshuffle his pack.
In came defender Thomas Rogne, midfielder Beram Kayal and striker Anthony Stokes.
Dons boss Craig Brown gave competitive debuts to former Celtic wide man Niall McGinn, Jonny Hayes and Gary Naysmith, the latter being lucky to escape an early booking for a lunge at Kayal.
In the 10th minute Celtic's stand-in skipper Georgios Samaras was caught with a flying boot from Aberdeen defender Ryan Jack but resumed after treatment to his bloodied face and with a new shirt.
The experienced visitors looked composed and confident for the most part and capable of striking on the break.
Dundee enjoyed a respectable return to the SPL as they claimed a point after holding Kilmarnock to a goalless draw in their season opener.
Their route to the SPL may have been unusual and controversial in the eyes of some but Dundee demonstrated an ability to hold their own following a seven-year absence from the top division, with both sides creating chances and Rab Douglas in the Dundee goal particularly impressive.
However, in the 21st minute Langfield was forced into a decent save from Commons' 25-yard drive after the Scotland midfielder had combined with Kayal.
Moments later, Samaras curled a shot from the left-hand side of the box which went just wide of the far post.
There was little more of note until 10 minutes from the break when Commons set up Gary Hooper but the former Scunthorpe striker ballooned his effort from the edge of the box over the crossbar.
Celtic defender Victor Wanyama had to move sharply at the other end to stop an Aberdeen counter-attack which involved McGinn and ended with the Northern Irishman racing desperately to get on to a Jack pass inside the box.
Aberdeen had a half-chance soon after the restart when Hayes' corner from the right was punched only as far as Dons striker Scott Vernon but from 12 yards he drove the ball high and wide.
Samaras, perhaps struggling from his early knock, was replaced by Kelvin Wilson in the 55th minute with Wanyama moving into midfield but Celtic could not shrug off their sluggishness.
Commons again took it upon himself to inject some excitement into the match in the 63rd minute, firing in a low 25-yard drive which Langfield saved down at his left-hand post.
The home fans became increasingly exasperated as the out-of-sorts champions huffed and puffed with decreasing success.
Fans' favourite Paddy McCourt replaced Kayal with 20 minutes remaining, with the Dons bringing on Chris Clark for Naysmith minutes later.
Lennon's last throw of the dice came when he threw on striker Daryl Murphy for Stokes and two minutes later the Hoops were in front when Langfield allowed Commons' shot to squirm through his hands at the near post.
The relief among the home fans was palpable and they, like the Celtic players, were happy to see the game out before they start preparing for their Champions League encounter in Finland.
Hearts secured a less-than-comfortable 2-0 win over St Johnstone at Tynecastle despite playing over half of the match against 10 men.
John Sutton's 30th-minute penalty and a late David Templeton strike separated the two sides with Saints' striker Gregory Tade shown a red card for a scuffle in the box six minutes before half-time.
Ross County extended their unbeaten league run into the top flight as a goalless draw with Motherwell made it 35 games without defeat.
County produced a solid SPL debut and restricted Motherwell to very few chances at the revamped Global Energy Stadium in Dingwall.
Motherwell had the better of possession but last season's Irn-Bru First Division champions looked a threat from set-pieces with some dangerous deliveries by Iain Vigurs and Richard Brittain offering opportunities to tall defenders such as Ross Tokely and Grant Munro.
Darren McGregor's stoppage-time header salvaged a point for St Mirren from an entertaining 2-2 draw with Inverness at St Mirren Park.
Debutant Lewis Guy had given the hosts the lead just after the half-hour mark with an accurate angled drive beyond Ryan Esson but two goals in the final 20 minutes from Nick Ross and Billy McKay had appeared to have handed the visitors all three points.
However, McGregor was in the right place at the right time to head home when Esson completely misjudged a cross from the right.
In the aftermath of the goal, Saints were reduced to 10 men as Guy was sent off for clashing with Ross Draper in his attempt to get the ball out of the net.
- Jamie Langfield
- Champions League