The 31-year-old attacking midfielder combined with Anthony Stokes in the sixth minute to fire past Zagreb keeper Eduardo but the more than decent Croatian side came back and before the break their Portuguese forward Wilson Eduardo hit the bar with a long-distance drive.
The home side were on the back foot for long spells with goalkeeper Craig Gordon having another impressive night in the Hoops goal making several crucial saves but in the end Ronny Deila's side held out for the victory.
The Hoops had started the section with a creditable 2-2 draw away to Salzburg and next for the Scottish champions is a double-header against Romanian outfit Astra, with the possibility of reaching the 10 point-mark that Deila believes will ensure qualification.
Commons was back from an injury to his buttocks while defender Jason Denayer and wide-man Aleksandar Tonev were also restored to the starting line-up, striker John Guidetti again missed out as he was not registered in time for the group stages of the competition.
The match had not captured the imagination of the Hoops fans as the top tier of the 60,000-capacity stadium lay closed but those who did turn up cheered loudly a wonderful goal from Commons.
The former Nottingham Forest and Derby player cleverly stepped over a pass from left-back Emilio Izaguirre and then ran on to Stokes' perfectly-weighted through ball before rifling low past Zagreb keeper Eduardo from 12 yards.
Surprisingly, the game went a little flat after that which allowed the Croatian side to compose themselves again.
In the 19th minute Wilson Eduardo, Dinamo's most dangerous player in the first-half, headed an Ivo Pinto cross over the bar from 10 yards and then, in the 28th minute, he sent a drive from 25 yards whistling past Gordon only to see it rebound off the bar with Parkhead defender Virgil van Dijk helping to clear.
Four minutes later, however, Celtic should have been two up when Eduardo, in a moment of careless indecision, gifted possession to Commons six yards from goal but his pass to the better-placed Stokes was over-hit and the visitors survived.
The game moved from end to end.
A mistake by Parkhead full-back Efe Ambrose gave Wilson Eduardo the chance to fizz a volley from just inside the box towards goal but Gordon dived to his left to punch clear.
Two minutes from the break Eduardo beat away a powerful drive from the advancing Van Dijk with Zagreb skipper Josip Simunic completing the clearance.
Celtic midfielder Stefan Johansen had the home fans on their feet when burst into the Zagreb box seconds after the restart but he could not get the ball properly under control and was eventually outnumbered by defenders.
The visitors had a great chance to level in the 54th minute when a mix-up in the Hoops defence resulted in Wilson Eduardo having only Gordon to beat but the former Hearts and Sunderland keeper pulled off a tremendous point-blank save.
Dinamo had a firm grip of the game with a steady stream of pressure forcing Celtic towards their own box.
The Hoops defended well but occasionally Zagreb got through and in the 68th minute Gordon pushed a shot from Marcelo Brozovic past the post and then gathered the subsequent corner with ease.
As the match slipped into its fraught final stages, Stokes' in-swinging free-kick into a packed penalty area ended up in the arms of the grateful Eduardo.
There was time for Gordon to save from El Arbi Hilal Soudani before the Zagreb wide-man missed the target from six yards, with the home side forced into desperate defending only in the final few minutes.
Source : PA
Source: PA