Chilean Sanchez, who nearly left the club to join Manchester City on transfer deadline day, picked the ball up outside the area and curled a shot past keeper Timo Horn.
The game did not begin until 21:05 BST as thousands of visiting supporters arrived at the ground without tickets and then clashed with stewards inside the Emirates Stadium.
When the match did get under way, Cologne took the lead in spectacular fashion as Jhon Cordoba lobbed fellow Colombian David Ospina from 40 yards.
Striker Olivier Giroud planted a header wide of goal from six yards for the much-changed home side, who were booed at the half-time whistle.
But substitute Sead Kolasinac equalised with a thumping volley before Sanchez struck, and Hector Bellerin then added the third from close range, as midfielder Jack Wilshere made his first appearance for the club since August 2016.
In Group H’s other game, Red Star Belgrade drew 1-1 against BATE Borisov.
Who was your man of match???