A deflection and an own goal helped Arsenal overcome Celtic in Glasgow to leave the Gunners with one foot in the Champions League group stages.
Arsenal took the lead two minutes before the break when William Gallas inadvertently diverted a Cesc Fabregas free-kick past Artur Boruc, and Gary Caldwell put through his own net in the 71st minute.
Only Barcelona and Dinamo Moscow, in the previous round, had beaten Celtic in the previous 36 European matches at Parkhead.
But Arsene Wenger's side enjoyed a comfortable second half to leave them in a commanding position ahead of next week's play-off second leg.
Barcelona have also lost at Celtic Park during that run, along with the likes of Juventus, AC Milan and Manchester United, but Celtic failed to put their latest visitors under serious pressure.
Although both sides had enjoyed comfortable away wins in their opening league wins on Saturday, Celtic manager Tony Mowbray opted for radical alterations to his frontline while Arsenal were unchanged following their 6-1 win at Everton.
Mowbray dropped Scott McDonald and Marc-Antoine Fortune and played Aiden McGeady up front alongside Georgios Samaras, who scored the stoppage-time winner against Dinamo Moscow in Russia in the previous round.
Scott Brown came into right midfield while Caldwell returned after missing Saturday's 3-1 victory at Aberdeen through suspension.
Arsenal looked more comfortable in possession from the start, finding space in front of Celtic's back four.
Andrey Arshavin was causing problems when he drifted in from his position on the left of Arsenal's three-man attack, and Fabregas and Denilson were always looking to break forward from midfield.
Arsenal were playing the ball through Celtic and it needed a last-ditch block by Caldwell on Robin van Persie to stop the Gunners profiting from one such move, with the offside flag raised before Arshavin fired home the rebound.
However, Celtic had a good chance to hurt Arsenal on the counter-attack when Shaun Maloney released McGeady down the left after Van Persie's free-kick was cleared.
The Republic of Ireland international rode one challenge and lofted the ball towards Brown but Thomas Vermaelen did enough to put the midfielder off.
Celtic tightened up in central midfield, although a slip by Massimo Donati allowed Arshavin the chance to run at the Celtic back four, with Boruc getting down comfortably to save his deflected effort.
Full-back Andreas Hinkel then created Celtic's best chance of the half when he burst into the box and cut the ball back for Maloney.
The Arsenal defence closed him down but the ball fell for Brown, whose low shot was well saved by Manuel Almunia.
Celtic looked like they would comfortably survive until half-time but luck was against them after Caldwell was penalised for a foul on Fabregas 30 yards out.
The free-kick was rolled short to the Spaniard, whose 30-yard drive bounced off the back of Gallas and spun into the opposite corner to where Boruc was heading.
The game almost drifted beyond Celtic within a minute of the restart after Landry N'Guemo miscontrolled a simple take in the centre circle.
Arshavin carried the ball to the edge of the penalty box before slipping the ball outside to Van Persie but the Dutchman shot past the far post.
Denilson soon curled just wide from 20 yards following another Arshavin run while Fabregas dragged a left-footed shot just wide from a similar distance after Gallas had easily won a 50-50 challenge with Donati.
McGeady had dropped deeper after the interval and Mowbray made a double switch in the 56th minute with McDonald and Fortune replacing Donati and Samaras.
Celtic struggled to create chances but Gallas made another crucial interception when he cut out Fortune's low cross as McDonald waited at the far post.
Abou Diaby replaced Arshavin and immediately played a key role in Arsenal's second goal.
The substitute burst forward and set up Gael Clichy for a low cross that was turned home by the outstretched boot of Caldwell.
Only McGeady looked capable of creating anything for Celtic and most of the final 20 minutes was played out in the middle third.Reuse content