Kick-off in the Group H opener at the Emirates Stadium was put back until 9:05pm local time (2005 GMT) in the interests of "crowd safety" after problems caused by thousands of ticketless Cologne supporters arriving at the ground.
Gunners beat Cologne 3-1 in Europa League
After a lacklustre first half, Arsenal scored three goals in the first to kickoff their Europa League campaign with a win.
Police confirmed four arrests were made before kick-off while there were reports of scuffles inside the stadium.
However, when the match did get under way, those travelling fans who got in were treated to a stunning 40-yard strike by Jhon Cordoba that put Cologne ahead with Arsenal goalkeeper David Ospina caught out of his area.
Arsenal improved in the second half and substitute Sead Kolasinac volleyed them level before a brilliant goal by Sanchez gave them a 67th-minute lead.
The Chilean cut in from the left flank before curling a sublime effort into the far top corner, and the three points were secure when Hector Bellerin made it 3-1 late on after Theo Walcott's effort had been saved by Timo Horn.
Arsenal's Chilean striker Alexis Sanchez passes the ball during the UEFA Europa League Group H football match against FC Cologne at The Emirates Stadium in London on September 14, 2017
"The win, and coming back from losing, obviously gives you a boost. Now we'll train hard in the coming days to be ready for the weekend," Bellerin, whose side go to Chelsea on Sunday, told BT Sport.
Arsene Wenger's side are next in European action in a fortnight in Belarus against BATE Borisov, who drew 1-1 at Red Star Belgrade.