After winning 2-0 in Enschede two weeks ago, the Gunners were always strong favourites to take their place in Thursday evening's draw, and there was never any doubt about the final outcome.
Despite making a bright start to the second leg, Steve McClaren's side were outclassed and in truth the Gunners could have won the Emirates Stadium clash by a far wider margin.
Cesc Fabregas was able to start his first game of the season after recovering from a hamstring injury and the Spaniard had a major influence on the match, as did the lively Theo Walcott.
The Dutch side settled well and dominated possession in the early stages but, from the tenth minute onwards, Arsenal took control.
Johan Djourou lashed a ten-yard shot wide in the 17th minute and, six minutes later, Fabregas burst down the left and pulled the ball back for Robin van Persie to lash a 15-yard effort over the bar.
The Gunners took the lead in the 27th minute. Walcott's speed and trickery caused the Twente defence to back off and, when the ball broke to Samir Nasri, the young Frenchman showed some good skill of his own before clipping his shot home.
There could have been more goals before the interval as Nikolaj Mihajlov was forced to save the unmarked Denilson's drive with his legs before Walcott set up van Persie who somehow contrived to miss the target when he seemed certain to score.
The one-sided nature of the game continued after the break and Arsenal eventually doubled their lead in the 52nd minute.
A powerful run by William Gallas caused the Dutch side's defence all sorts of problems and, after Mihajlov had saved Nicklas Bendtner's shot, the ball broke to the Gunners captain who stabbed the rebound into an empty net.
It was 3-0 on the night and 5-0 on aggregate 14 minutes later when Arsenal launched a quick counter-attack. As the hapless Twente defence parted, Walcott was able to glide forward before placing his shot past Mihajlov.
Wenger's side cruised through the rest of the match but were still able to add a late fourth goal when Bendtner netted after being set up by Denilson's precise back-heel.