Commons pounced 13 minutes from time when he headed home Emilio Izaguirre's cross to give Celtic a slender advantage ahead of next week's return in Sweden.
In the first half, James Forrest was denied by the woodwork and Anthony Stokes had an effort ruled out for offside, while Anders Svensson struck the crossbar for Elfsborg.
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 in front of a decent crowd inside Celtic Park.
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.
Forward Derk Boerrigter, who signed for Celtic from Ajax on a four-year deal subject to international clearance on Tuesday, was not involved at all as the Hoops kept the same 11 which beat Cliftonville at home in the previous round, with Stokes leading the line.
Within seconds of the kick-off the Irishman latched on to a Georgios Samaras head-flick which breached the Elfsborg defence and volleyed across goal from a tight angle, the ball fizzing past the far post.
Strangely, Celtic looked anxious for the following few minutes allowing Elfsborg, with Bangura bustling and busy, to get a foothold in the game.
In the 15th minute Commons volleyed high over the bar from 12 yards after another good run by Samaras down the left-hand side.
After Forrest hit the bar with a volley from Commons' cross, Stokes had the ball in the net from a pass from the former Derby player but the flag was already up for offside.
The Swedish side grew in confidence as the first-half flowed from end to end exemplified by Svensson's thunderbolt which crashed off the crossbar.
However, Hoops defender Efe Ambrose should have put Celtic ahead but headed a Commons' corner over the bar from six yards when he should have at least hit the target.
In first-half injury-time, Commons was fouled by Johan Larsson 20 yards from goal which led to Stuhr-Ellegaard having to make a good save from Stokes' free-kick at the expense of a corner which came to nothing.
The Hoops came out for the second half somewhat energised and a minute after the restart Samaras found himself with the ball at his feet eight yards out but hit it straight at Kevin Stuhr-Ellegaard.
There was an unsuccessful Celtic appeal for a penalty in the 65th minute when Samaras' shot was deflected past by Elfsborg defender Daniel Mobaek, just before Joe Ledley replaced Beram Kayal.
Bangura further irked the home fans when he went to ground after a harmless-looking tussle with Kelvin Wilson on the touchline with Portuguese referee Manuel Se Douda unimpressed.
It was proving to be hard work for Celtic, as Elfsborg dropped deeper looking to hold out for the draw.
However, Commons' goal gave Celtic the lead they desired and, as they pushed hard for the second goal, a Samaras header was cleared off the line by Andreas Klarstrem.
After away victories at HJK Helsinki and Helsingborgs in last season's qualifiers, Celtic will travel to Sweden for the second leg with added confidence, although manager Neil Lennon will be looking for some improvement.