The Gunners barely looked in danger of conceding throughout the evening, until the last kick of the match when Massimo Donati scored from the tightest of angles in a freak moment.
Despite their dominance, the home side had to rely on the cunningness of Eduardo to give them the lead as the Croatia international won a penalty with a dive around the clutches of innocent Celtic goalkeeper Artur Boruc.
After some delightful interplay, Eduardo skipped into the penalty area past the helpless Hoops defenders, but crashed to the ground as Boruc edged to his boots to sweep the ball away.
Replays confirmed that there was no contact, but Spanish referee Manuel Gonzalez pointed to the spot.
Eduardo took it upon himself to slot the penalty home just before the half-hour mark, leaving Boruc infuriated.
A rare piece of Celtic attacking play ended with the ball in the back of the 10 minutes later, as Marc-Antoine Fortune's cross found Scott McDonald who stroked home. However, he was rightly adjudged offside to dash hopes of a Celtic comeback.
The second period carried on much like the first, as Celtic's approach of playing Arsenal at their own game failed to pay off.
It was the men in red who continued to create the openings and the tie was sealed once and for all just eight minutes after the break.
Emmanuel Eboue's goal highlighted the gulf in class between the two sides, as the build up to the strike was vintage Arsenal.
Nicklas Bendtner's delightful back-flick near the left touchline released Abou Diaby who had a free run into the area. He squared for Eboue, who was magnificent throughout, and the defender-cum-midfielder in turn controlled and stroked home from 12 yards.
From then on, the match was played at a pedestrian pace and it was exhibition stuff from the Gunners.
Substitute Andrey Arshavin netted with his first touch of the game by spinning around Donati to stroke home, with youngster Aaron Ramsey providing the assist with a soft lay-off after Denilson's charging run.
Celtic were granted an injury time consolation as they prepare for an assault on the UEFA Europa League.
Donati latched onto Andreas Hinkel's ball on the far side of the penalty area to stretch his left leg out for a volley. He caught it sweetly and Manuel Almunia could only look on as it went across him into the corner of the net, with the last kick of the game.