The Bhoys travelled to Sweden protecting a slender one-goal lead - given to them by Kris Commons at Celtic Park last week - and were able to secure a 0-0 draw at the Boras Arena.
Despite seeing little of the ball in the first half, it was the visitors who had the better opportunities.
Greek striker Giorgos Samaras then ballooned a header over the bar from around 12 yards out, while Elfsborg had goalkeeper Kevin Stuhr Ellegaard to thank for keeping them level, as Neil Lennon's men came close to scoring in the 20th minute.
Mohamed Bangoura - on loan from the Scottish champions - also fluffed his lines with a close-range header, which meant that the teams went in at half time goalless.
The home side pressed for an equaliser in the second half, but Celtic's back line held firm, restricting their opponents to speculative efforts. body check tags ::