William Gallas knew very little about Arsenal's opening goal on the stroke of half time, when a fiercely struck Cesc Fabregas free-kick deflected off the Frenchman to wrong-foot Celtic keeper Artur Boruc and put the Gunners ahead.
And Arsene Wenger's side extended their lead to put the tie almost out of Celtic's reach when Gary Caldwell inadvertently directed a hopeful ball into his own net on 70 minutes to give Arsenal a second away goal.
On the final whistle the Celtic Park crowd showed their appreciation for a home performance that matched the English side in possession and passion, but they know a miracle is needed if their team are to progress to the next stage for the competition.
In an even first half, the game looked likely to be deadlocked at the interval before the lucky intervention from Gallas.
A free-kick awarded just outside the Celtic box on 43 minutes was rolled to Fabregas by Robin van Persie and the Spaniard crashed a shot goalwards.
Boruc looked to be making his ground to enable a routine save but the ball struck Gallas on the back as he tried to avoid making contact, sending the ball spinning into the opposite corner of the Celtic net.
It was rough justice on Tony Mowbray's side but they could easily have found themselves further behind immediately after the break after a sloppy start to the second half.
Van Persie should have done better with a gilt-edged chance moments after the restart before Denilson flashed an effort just wide.
Celtic one again managed to work their way back into the game but it was Arsenal who put themselves in pole position in the tie when Caldwell diverted Gael Clichy's hopeful cross past Boruc in the 70th minute.
Good work by substitute Abou Diaby set Clichy free down the left and his first-time ball posed a problem for Caldwell at his near post with van Persie lurking.
The Scotland defender opted to stretch for the interception and could only watch in agony as the ball ricocheted off the sole of his boot and past Boruc, putting Arsenal within touching distance of the Champions League group stage.