A debut goal from Dedryck Boyata right on the stroke of half time has given Celtic a narrow lead over Stjarnan in the first leg of their Champions League second qualifying round at Celtic Park.
The hosts created the first opening of the match inside 10 minutes when Stefan Johansen pounced on a loose pass and found Nadir Ciftci, but the debutant striker was denied by Gunnar Nielsen in the Stjarnan goal.
As expected, it was Celtic who were asking the majority of the questions, and they squandered another clear chance to break the deadlock midway through the half when Johansen dragged a shot wide after the visitors had failed to clear Charlie Mulgrew's cross.
The pressure continued to build on the Icelandic minnows, but they held firm despite Stuart Armstrong sending a long-range effort fizzing just over before drawing a fine stop from Nielsen.
Ciftci then came close again with a glancing header as Celtic enjoyed total domination but struggled to break through their resilient opponents.
However, the visitors were unable to hold on until half time as Celtic finally opened the scoring a minute before the break when Boyata powered a header home on his debut.