Arsene Wenger had been forced to name a young side for the first left of this qualifier, which included a competitive debut for 17-year-old Aaron Ramsey.
But it was the experience of captain William Gallas and Togo striker Emmanuel Adebayor which proved decisive with two opportunist strikes in the second half.
• Wenger happy after mature win
The Gunners had been pressed onto the back foot for most of the opening hour by the Dutch side, who played with the panache which ironically England had lacked under the stewardship of McClaren.
With a comfortable cushion to defend at the Emirates Stadium in a fortnight's time and a place among Europe's elite all but assured once more, the Barclays Premier League club can now turn their attentions to getting the domestic campaign off to a similar positive start against West Brom on Saturday.
With the Grolsch Veste undergoing refurbishment, the match was effectively an away tie for both teams.
However, the 25,000 Twente fans did their best to make themselves feel at home with a rousing rendition of `You'll Never Walk Alone' greeting the players as they ran out at the Gelredome.
The weather had settled following earlier torrential rain, giving almost perfect conditions for what promised to be a fascinating tactical battle between Wenger and the former England head coach, whose reign ended under an umbrella on a wet November night at Wembley.
It was a bright start by the Dutchmen, with Roman Denneboom heading wide at the far post following a deep cross from the left.
Arsenal - who have played in the Champions League proper for more than a decade - slowly began to find their rhythm, but were unable to break down Twente.
The Dutch continued to look dangerous on the counter-attack with some slick passing moves.
After 18 minutes, Eljero Elia almost got on the end of a pass into the left side of the Arsenal area, but keeper Manuel Almunia slid out to make a brave block.
Denneboom should have done better when, in the 25th minute, he weaved his way into the penalty area - only to fire a shot high over the crossbar.
As the half-hour mark approached, Arsenal continued to be pushed back with Ramsey, aiming to fill the void left by an injured Cesc Fabregas, and Denilson, the Brazilian youngster, not able to get hold of the ball in midfield.
When the young Welshman was set up with a shooting chance following a free-kick, his effort from 25 yards flew wide.
FC Twente wasted another golden chance when Marko Arnautovic dashed clear only to lose control on the edge of the area, which allowed Almunia to make the save.
Arsenal's real first decent opening came in the 38th minute.
Goalkeeper Sander Boschker could only parry a fierce 25-yard drive from Gael Clichy, which fell to full-back Bacary Sagna in the six-yard box - but his snap shot was just off target.
There seemed more urgency about Arsenal following the restart, with Robin van Persie having his shot charged down on the edge of the Twente penalty area.
Twente, though, were soon back in the ascendancy, playing with a confidence and flair which McClaren's England side had so often lacked.
However, Arsenal snatched a crucial away goal in the 63rd minute, after Emmanuel Eboue was adjudged to have been fouled on the right - much to the disbelief of McClaren.
Van Persie's free-kick floated through to the six-yard box, where Gallas bundled the ball in to the net.
To their credit, Twente continued to press, and Arnautovic pushed his shot wide from an acute angle after being put in on the left side of the penalty area.
Arsenal, however, remained patient as the tempo of the match dropped heading into the closing 10 minutes.
The victory - and surely a place in the Champions League group stages - when Theo Walcott dashed into the right side of the Twente area before finding Adebayor, who rolled his shot under Boschker.
Wenger happy after mature win
Arsene Wenger was pleased to have seen his young Arsenal side come through a tough 'physical' test as they beat FC Twente 2-0 in Arnhem to move a step closer the group stages of the Champions League.The Gunners had been pressed onto the back foot for most of the opening hour by
the Dutch, now under the guidance of former England head coach Steve McClaren.But for better finishing from Romano Denneboom and Marko Arnautovic - who both
missed good chances in the first half - the Premier League side could have been
facing an uphill battle to continue their decade-long run among the elite of
European football.However, slowly Arsenal - who had Wales teenager Aaron Ramsey making a full
debut in central midfield because of injury to Cesc Fabregas - got a foothold in
the game and took the lead when captain William Gallas bundled in a deep
free-kick from Robin van Persie just after the hour.Togo striker Emmanuel Adebayor netted a second with eight minutes left to put
the Gunners in command of the tie.'They imposed a very physical game on us, with man marking all over the pitch.
They did that with a lot of belief and spirit,' said Wenger.'In the first half, they had some chances, but in the second half we slowly
took over.'They have given so much in the first half, they could not keep the same pace
and tightness in their marking.'From then on, we looked more comfortable.'Wenger added: 'We were a very young team and we did not lose our nerve, did
not panic.'In the end maybe our technical superiority allowed us to score two goals -
that is a massive advantage for the second leg, but we will be on our toes.'McClaren - whose England reign ended under an umbrella on a wet November night
at Wembley - was happy enough with the effort shown by his team.However, without suspended striker Blaise Kufo and injured frontman Youssouf
Hersi, Twente paid the price for lack of a cutting edge in front of goal.'We said that in Europe against the top teams you don't get many chances and
you have to take one. We failed to do that and we got punished,' the former
Middlesbrough coach reflected.'We had a bad spell of 10 minutes in the second half, lost concentration and
we conceded that first goal which deflated us - but credit to the team, they
kept going.'I think Arsenal will come away absolutely delighted with the result.'You saw a performance of great spirit and Arsenal were rattled, they know
they have been in a game.'McClaren added: 'We are so disappointed, but proud of the performance.'It just showed our inexperience in Europe in key moments and key occasions
that we lost this game.'We have a hell of a mountain to climb now, but we just need to put in another
good performance.'This team will learn a lot and be better for it.'
Twente Enschede 0 - 2 Arsenal
