By Chris Harris at Emirates Stadium
Danny Welbeck scored his first senior hat-trick as Arsenal marked Arsene Wenger's 18th anniversary as manager with an emphatic win in the Champions League.
The deadline-day signing poked in his first goal after 22 minutes and added a second on the half-hour mark after powering clear of the Galatasaray defence.
Alexis Sanchez grabbed a third just before half-time after latching onto Mesut Ozil's through-ball, and Welbeck completed his treble with another deft finish early in the second half.
There was one setback, Wojciech Szczesny receiving a red card for conceding a penalty that Burak Yilmaz converted with 27 minutes left, but the Gunners saw the game out comfortably enough with 10 men.
Welbeck will hog the headlines and rightly so. This was a performance of pace, power and intelligent movement that demonstrated why Wenger sees the 23-year-old as a centre forward and not a wide man.
Arsenal's organisation and work ethic was equally welcome, and they are now heading in the right direction in Group D, second behind Borussia Dortmund after two games.
Wenger insists he "doesn't look back" when he thinks about his 18 years at the helm, but he will surely allow himself time to reflect on an almost perfect performance - and Welbeck's 'coming of age' in an Arsenal shirt.
SETTING THE SCENE
The manager made three changes for Arsenal's second Group D fixture - all of them enforced.
Mikel Arteta, Aaron Ramsey and Jack Wilshere were hurt during Saturday's north London derby and, although the latter made the squad, he started on the bench. In came Santi Cazorla, Mathieu Flamini and Alexis.
Wenger's 1,022nd match as Arsenal manager marked his 18th anniversary at the helm, and it was one his team really had to win. A 2-0 defeat at Borussia Dortmund on matchday one had left the Gunners playing catch-up.
Galatasaray made a sluggish start of their own in Group D, drawing 1-1 at home to Anderlecht, and although the Turkish giants won the Emirates Cup last year, they were without a win in nine competitive games on English soil.
These teams had met once before in European competition - the 2000 Uefa Cup final, when Galatasaray prevailed after penalties.
Arsenal started on the front foot with Alex Oxlade-Chamberlain prominent and Cazorla prompting from a deeper role than usual.
Ozil had a loose ball taken away from him as he prepared to let fly inside the box and Welbeck turned on the afterburners to race clear of two markers before eschewing the obvious pass to Ozil and shooting tamely.
The home side looked bright and energetic but Alex Telles had the clearest sight of goal in the first 10 minutes, losing Calum Chambers and sweeping a shot just wide of the far post.
Galatasaray looked useful with their own deep-lying playmaker, Wesley Sneijder, dictating their play, but Arsenal contained the visitors and then hit them with a slick move in the 22nd minute.
Kieran Gibbs found Alexis and he cut inside his man before picking out a diagonal burst from Welbeck with a perfectly-weighted through-ball. Welbeck did the rest, poking the ball between Fernando Muslera's legs.
Welbeck's clever movement and quick feet were troubling the Galatasaray defence and he almost profited again after Ozil nudged the ball through to him on the edge of the box.
Alexis dragged another effort wide before Welbeck doubled his tally on the half-hour mark. If his first goal was about movement, this was about power and pace as Welbeck outmuscled Felipe Melo and strode clear before beating Muslera.
His confidence flowing, Welbeck almost completed his hat-trick three minutes later with a low shot that Muslera saved.
Goran Pandev reminded Arsenal of Galatasaray's latent threat with a shot that Szczesny got down well to save, but the visitors' main source of danger was at the other end, where their boisterous fans caused a stoppage by throwing flares onto the pitch.
Melo almost followed the flares off the pitch but escaped with a yellow card after a nasty two-footed challenge on Alexis. It took a while for the smoke and tempers to die down but Alexis responded in the best possible way, running onto Ozil's fine pass to add a third goal.
Alexis was influential at the start of the second half too, his exquisite pass releasing Oxlade-Chamberlain down the left. The England international beat Melo for pace but his cut-back was cut out.
Moments later, Welbeck took centre stage once again.
He started a move on the left flank and, by the time the ball reached Oxlade-Chamberlain outside the box, Welbeck was in position to make another intelligent dart in behind the Galatasaray defence.
""Danny Welbeck, he scores when he wants!" was soon ringing out at the Emirates"
Oxlade-Chamberlain timed his pass perfectly and Welbeck lifted the ball over Muslera. "Danny Welbeck, he scores when he wants!" was soon ringing out at the Emirates.
The points were effectively secure but Arsenal's task suddenly became more onerous when Szczesny was sent off for denying Burak a goalscoring opportunity after the Turkish forward surged into the box.
Burak beat substitute goalkeeper David Ospina with a confidently struck spot-kick, and Galatasaray had 23 minutes in which to launch the mother of all comebacks.
Sneijder went as close as anyone to making that dream a reality with a low shot that had Ospina scrambling across his goal, but Arsenal had opportunities at the other end too, Welbeck heading a difficult chance over the bar.
Ospina clawed away a powerful Burak header with 10 minutes remaining and then blocked with his legs when Hamit Altintop found space to unleash a fierce drive.
Sneijder went close again with five minutes left and a Galatasaray goal then might have set up a grandstand finish.
But Arsenal took the sting out of the match, and took the points.
Referee: Gianluca Rocchi
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