It was not a vintage performance from the Hoops who huffed and puffed for long spells against the organised and at times robust Swedish champions.
Both sides hit woodwork in an open and even first 45 minutes.
In the 20th minute Celtic wide-man James Forrest struck the bar with a volley which first bounced off the ground, following a whipped-in cross from Commons.
However, the visitors grew in confidence as the game went on and skipper Anders Svensson rattled the Celtic bar from 25 yards in the 31st minute, before heading over from a Stefan Ishizaki corner moments later.
Celtic had more of the play and possession in the second-half and got the breakthrough when Emilio Izaguirre planted a cross on to the head of the former Nottingham Forest player who planted it past keeper Kevin Stuhr-Ellegaard.
Much of the attention was on Mo Bangura, who, as expected, took his place in the Elfsborg side against his parent club who had tried and failed to prevent the 24-year-old striker, on loan to the Swedes for one year, from playing in either of the ties.
Bangura was jeered each time he touched the ball but kept the Celtic defence occupied without causing material damage, although after getting stick from the home fans until he was substituted late in the game, he will be determined to do better next week.
However, Commons’ goal should be enough to see Celtic into the play-offs.
And after away victories at HJK Helsinki and Helsingborgs in last season’s qualifiers, Celtic will travel to Sweden next week for the second-leg with added confidence although manager Neil Lennon will be looking for some improvement.
“I would have taken any kind of lead,” Lennon said. “I thought we played well and maybe deserved a bigger lead. I’m pretty pleased. Overall, the attitude of the players was fantastic.”
CELTIC: Forster, Izaguirre, Ambrose,Wilson, Lustig, Brown, Commons, Kayal (Ledley 66),Forrest, Samaras (Mulgrew 86), Stokes.
ELFSBORG: Stuhr-Ellegaard, Jonsson, Klarstrom, Larsson, Svensson, Mobaeck, Hauger, Ishizaki (Jorgensen 85), Rohden, Keene (Hult 80), Bangura (Nilsson 81).
Referee: Manuel de Sousa (Portugal)
Last night’s Champions League results: Apoel Nicosia 1 Apoel Nicosia 1, Molde 1 Legia Warsaw 1, Ludogorets Razgrad 2 Partizan Belgrade 1, SV Salzburg 1 Fenerbahce 1.