Summer signing Danny Welbeck was the hero for the ten-man Gunners with a hat-trick in just his fifth start for his new club.
The former Manchester United man finished coolly on two occasions in the first half before completing his treble early in the second half to give the north Londoners a four-goal lead before their Turkish opponents grabbed a consolation.
Welbeck put Arsenal in front in the 22nd minute when he raced onto a through ball from Alexis Sanchez to slot past Fernando Muslera before adding a second eight minutes later when he headed forward before advancing into the area and again netting past the Galatasaray keeper.
Alexis got in on the act five minutes before the break when he received a pass from Mesut Ozil before cutting back in from the left and firing past Muslera's outstretched left hand.
Seven minutes into the second half and Arsene Wenger's side were four to the good thanks to Welbeck's third which was a deft little dink from Alex Oxlade-Chamberlain's clever ball making him the first Arsenal player to score a Champions League hat-trick since Nicklas Bendtner in March 2010.
On the hour-mark, Arsenal's night was dampened when goalkeeper Wojciech Szczesny was sent off for pulling down Burak Yilmaz in the area before the Turkey international sent substitute David Ospina the wrong way to give the visitors some semblance of hope.
Cesare Prandelli's Cimbom came hard at the ten-man Gunners in the final 25 minutes but Colombia international Ospina produced his brilliant World Cup form to keep out a number of strong chances, holding the score at 4-1 for the remainder.
2014/15 UEFA Champions League - Group D
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