Iain Macintosh: Welbeck is Wenger's best signing
(Danny Welbeck 22, 30, 52, Alexis Sanchez 41)
(Burak Yilmaz 63-pen)
The Arsenal fans who doubted the wisdom of spending £16 million ($33m) on Danny Welbeck must be feeling very silly now.
The Manchester United supporters who always cherished one of their own will look on with envious eyes.
This is the potential that they had always seen. This is what happens when a young striker of talent and intelligence is finally given a long run in his favoured position.
Put simply, Welbeck is the most important signing Arsenal have made in many years.
"I knew he was quick, but I didn't know he was this quick," beamed Arsene Wenger after the match.
"What is good for me is his link play, his teamwork, his work-rate, his attitude, it is very positive. He is not only a finisher, but also a team player."
Welbeck's hat-trick, made up entirely of well-taken, composed finishes, may have come against a weak Galatasaray side who self-destructed under the first sign of pressure, but it's a sign of what's to come from a striker with so much to prove.
Composure has always been the attribute he has been told he lacks, but there was nothing wrong with his finishing here. The Turkish giants were simply ripped apart.
"Welbeck was on the end of good movement tonight," said Wenger.
"We had good pace in our game and our transition was good. Danny was at the end of good collective movements.
"That was good to see, he slowly gains confidence, he finishes well, the potential is there. Hopefully, this hat-trick will help him to gain confidence."
Galatasaray boss Cesare Prandelli is not unaccustomed to good teams falling apart without warning.
His Italian side started the 2014 World Cup like favourites and then crashed out of the group stage.
There was something of that disintegration here. Welbeck's first goal, struck in the 22nd minute, snuffed out their resistance. His second, eight minutes later blew their focus completely.
Felipe Melo should have been sent off for a horrendous challenge on Alexis Sanchez, studs up and out of control.
The supporters began to hurl lit flares onto the pitch and the game was held up as stewards scurried around pouring buckets of sand on bright purple pyrotechnics.
Galatasaray's support, enlarged by numbers from London's Turkish community, were vibrant and noisy, even before the kick-off.
Thousands of them bouncing in the corner of the stadium that serves as an away end, scarves twirling, fists pumping, flares blazing.
They couldn't bring all of Istanbul with them to London, but it certainly sounded as if they'd stowed a significant chunk of it in their luggage.
But partisan support wasn't enough to keep Arsenal at bay and, four minutes before half-time, Galatasaray were three goals down and, this time, it was Sanchez who struck, again through the porous left side of the Turkish side's back three.
And this was an Arsenal side plagued with injuries, denied the use of their three first-choice midfielders, but the stand-ins did themselves proud.
Santi Cazorla was merrily dinking the ball around the pitch, Mathieu Flamini just about keeping his temper behind them.
Shifted back to the centre, Mesut Oezil gave a wonderfully subtle performance.
On the left flank, he can neglect his defensive responsibilities and drift out of the game but, in the middle, he has the flair and the brilliance to torment.
He may not always look like the most dynamic player on the pitch, but his movement and his vision stand out.
There are others who can clatter. Oezil should be left to create.
Welbeck completed his hat-trick after the break, but Arsenal were denied a comfortable finish when Wojciech Szczesny was dismissed and Burak Yilmaz converted the resulting penalty.
Still 4-1 down, Galatasaray sensed weakness and poured forward, revitalised and convinced there was a way back into the game. They were wrong.
Substitute goalkeeper David Ospina made a string of important, albeit rather untidy, saves that kept the opposition at bay.
With Borussia Dortmund crushing Anderlecht 3-0 in the group's other game, Arsenal can all but seal qualification to the next round by beating the Belgian side home and away in their next two fixtures, something for which they should be more than capable.
That will be a great weight off Wenger's mind.
With that, Oezil's performance and the hot streak of Welbeck, it was a very good night for Arsenal.
Wenger hails 'electric' Danny
Arsenal manager Arsene Wenger has no doubt that Danny Welbeck will continue to go from strength to strength after the striker's hat-trick in the Champions League win over Galatasaray in a match, which was stopped during the first half when Turkish fans threw flares (above) onto the pitch.
With England boss Roy Hodgson watching from the stands, Welbeck, the £16-million ($33m) deadline-day signing from Manchester United, produced a clinical display to set up a 4-1 win which puts the Gunners back on course for qualification from Group D and marks Wenger's 18th anniversary in style.
Welbeck's cool finishes had put Arsenal 2-0 ahead, before Alexis Sanchez swept in a third. The 23-year-old England man then completed a first career hat-trick on 52 minutes.
Arsenal finished with 10 men after goalkeeper Wojciech Szczesny was shown a red card for bringing down Burak Yilmaz, who rifled home from the spot.
Wenger has no doubts Welbeck can go on and take his game to another level, with Arsenal set to head to English Premier League leaders Chelsea on Sunday.
"It is good that slowly he gains confidence and finishes well. Hopefully, the hat-trick will help him gain confidence," said Wenger.
"It is not just his finishing because he wants to help the team. His team play is good as well, his teamwork and work-rate.
"I believe that, technically, he is very sound, a good passer of the ball.
"Honestly, I knew he was quick, but he can be electric when he starts - he has great pace."
Galatasaray coach Cesare Prandelli admitted that their approach had proved costly.
"We should have played more aggressively. The Champions League is a big tournament and we should come ready," the Italian said.
"It is important for us to understand where we made mistakes and where we can develop - it is up to us to correct it." - PA Sport.
On TNP tweets
>Jack Wilshere, Arsenal midfielder:
I told you all about Welbs!!!! Buzzing for him. Good win tonight! Thanks for the support as always! #OntoTheNext.
>Aaron Ramsey, Arsenal midfielder:
Great win tonight, looking forward to Sunday now. Buzzing for Welbeck.
>Mesut Oezil, Arsenal midfielder:
Our present for Monsieur Wenger's 18th Arsenal anniversary! #happy #UCL #AFCvGAL #GunnersOnFire pic.twitter.com/lp8LqIh5EI
>Lukas Podolski, Arsenal forward:
Amazing Champions League win tonight very proud of my team. Now big focus for Sunday's derby game!!! #AFC #UCL #Poldi #aha #RedArmy
>Gary Lineker, former England striker:
Just saw Welbeck's 3rd goal. Now that is the finish of a proper striker!