First-half goals from Samir Nasri and Denilson - both of which came via mistakes from visiting players - ensured the Gunners progressed as Group H winners with one match still remaining.
Arsene Wenger made five changes to the side that lost at Sunderland in the league on Saturday, but the likes of Cesc Febregas, William Gallas and Andrey Arshavin all started in a strong looking line-up.
There was no repeat of the horror start which the Gunners endured in Belgium on match-day one when they found themselves two goals down inside five minutes before bouncing back to win 3-2.
The home side roared out of the starting blocks and dominated possession with their trademark quick passing and intelligent movement.
Carlos Vela rattled the post when he followed up Arshavin's header from a 16th minute corner with a wasteful close-range shot.
However, the Gunners could have found themselves a goal down on 22 minutes when Dieumerci Mbokani clattered the angle of post and crossbar with a hopeful shot which came completely against the run of play.
However, Arsenal finally made the break through on 35 minutes when Landry Mulemo's costly slip let in Nasri, who found the back of the net with a composed finish.
That was the cue for the home side to turn the screw and Fabregas and Arshavin both went close despite the latter sporting a nasty head wound following a collision with Gallas which ended his team-mate's involvement at half-time.
Gallas was lucky not to give away a penalty on the stroke of half-time when he bundled Reginal Goreux over in the box only for a lenient referee to wave play on.
But the half ended on a high for the Gunners when Denilson's hopeful long-range strike was misjudged by the flailing Sinan Bolat and the goalkeeper was left red-faced as the ball flew into the back of the net to double the advantage.
The second half was effectively a footballing lesson for the Belgian side as Arsenal dominated possession while still playing comfortably within themselves.
Wenger sent on Theo Walcott and Rosicky for some much-needed match practice following their returns from long-term injuries.
Both showed neat touches in the final third as Arsenal toyed with their opponents, while Liege offered nothing as an attacking force.
The only moment of drama came right at the death when Liege forward Mehdi Carcela-Gonzalez became embroiled in a spat with Fabregas after a crude lunge and was sent off for a needless piece of violent conduct when he went head-to-head with the bemused Arsenal captain.