The Gunners turned up in Istanbul under a cloud after last weekend's shock Premier League opening loss to Aston Villa and inactivity in the transfer market
But goals from Kieran Gibbs, Aaron Ramsey and Oliver Giroud lifted the North London side past Fenerbahce in what beleaguered Wenger had described as "a massive" match.
The win, which puts Arsenal firmly in the driving seat for next week's return leg at the Emirates, will likely boost the club in their pursuit of their targets before the transfer window closes.
A relieved Wenger told Sky Sports: "It was a good performance in a heated atmosphere.
"We controlled the match and after the disappointment of the weekend we're in a strong position now. It was vital to get off on the right foot and that's what we did."
Ramsey added: "It was not the ideal start to the Premier League but we bounced back tonight - we have been criticised but we remained switched on. I'm feeling confident at the moment."
"We look very comfortable now for the second leg."
Walcott, looking ahead to the return leg, said: "We can't be complacent and have to be professional to get the job done."
The breakthrough after a dull opening half arrived in the 51st minute when Ramsey played in Theo Walcott down the right wing and the winger's cross was allowed to reach Gibbs who crashed the ball into the roof of the net.
Ramsey scored a fortunate second goal with 24 minutes left when Fenerbahce 'keeper Volkan Demirel inexplicably allowed a routine shot from outside the box slip under his hands
Giroud then planted a confident penalty in the top left hand corner after Michal Kadlec brought down Walcott on 77 minutes which has virtually put the tie beyond doubt.
Fenerbahce were looking to reach the pool stages despite a potential ban looming over them for match fixing that has gone to appeal and will be decided on the eve of the draw.
The only downside on an otherwise excellent night's work was the facial injury to Laurent Koscielny who had to come off.
Elsewhere Wednesday, there were 1-1 stalemates at the encounters between Steaua Bucharest and Legia Warsaw, and Schalke 04 and PAOK.
Swiss side Basel, beaten by Chelsea in the Europa League semi-finals last season, saw off Ludogorets Razgrad 4-2 while Austria Vienna defeated Dinamo Zagreb 2-0.