Wojciech Szczesny’s second-half red card was the sole blemish on a comfortable night for the Gunners that also saw Alexis Sanchez score and Burak Yilmaz net a consolation for Cesare Prandelli’s side.
Arsenal took the lead on 22 minutes when Sanchez cut inside from the left and angled a delicately-weighted through ball for Welbeck to poke through the legs of onrushing goalkeeper Fernando Muslera.
The home side doubled their advantage on the half-hour mark when Aurelien Chedjou failed to clear a long ball forward and Welbeck outmuscled Felipe Melo before confidently slotting home.
The former Manchester United forward almost had a third minutes later when Mesut Ozil’s clever lay-off found him in space 12 yards out but his left-footed shot was straight at Muslera.
Galatasaray’s fans were less than impressed with their team’s lacklustre first-half showing and referee Gianluca Rocchi was briefly forced to halt the game when they made their displeasure known by letting off red smoke bombs and launching flares onto the pitch.
The stoppage did little to deter Arsene Wenger’s side however and Sanchez made it three soon afterwards when he got on the end of Ozil’s through ball before stepping inside Chedjou and firing home.
Arsenal got their fourth on 54 minutes when Alex Oxlade-Chamberlain picked out Welbeck’s angled run behind the Galatasaray defence and the England striker produced a clever dinked finish to beat Muslera.
Szczesny was sent off on the hour mark when he hauled down Yilmaz in the box and Galatasaray’s top scorer dusted himself off to pull one back from the resulting penalty.
David Ospina came on in place of Sanchez following Szczesny’s dismissal and the Columbian produced an incredible flying save to keep out Yilmaz’s close-range header ten minutes from time.
The result moves Arsenal up to second in Group D on three points behind leaders Borussia Dortmund who enjoyed a comfortable 3-0 victory over Anderlecht in Belgium to maintain their 100 percent record.