Sanchez has cut a frustrated figure this season having seen a reported move to Manchester City fall through, but his moment of quality proved decisive on a bizarre Thursday night at the Emirates Stadium.
The game began amid swirling controversy, having been put back 60 minutes after a reported 20,000 Cologne fans descended on London despite only 3,000 tickets being available.
It appeared several were also in the Arsenal end, and they were quickly sent into raptures when Jhon Cordoba opened the scoring with a stunning 40-yard strike after nine minutes.
A lifeless atmosphere among the home contingent, depleted in numbers presumably because some fans opted to return home, was invigorated after the break as substitute Sead Kolasinac levelled.
And Arsenal ultimately condemned Cologne to defeat in their first European outing for 25 years thanks to Sanchez and Hector Bellerin's first goal of the campaign.
Any concerns the game may not go ahead would have been justified at one stage, with riot police inside and outside the stadium following the decision to delay kick-off.
But Arsenal suggested they were "comfortable" with the situation despite incidents of crowd trouble and the contest finally got under way at the revised time of 21:05pm BST.
Within 10 minutes, the hosts were anything but comfortable.
A hopeful long ball from Lukas Klunter had David Ospina racing from his line, but the Arsenal goalkeeper could only clear as far as Leonardo Bittencourt.
The midfielder made a hash of an attempt to control and the ball fell to Cordoba - who unleashed a stunning strike that flew over the back-pedalling Ospina and found the net.
The hosts had actually been on top prior to that intervention, a pattern that continued after the goal as Olivier Giroud twice went close.
Arsene Wenger introduced Kolasinac at half-time and the move paid immediate dividends as he hammered Arsenal level.
Theo Walcott got in behind the defence and, after his attempted pass deflected off Klunter and into the air, the left-back was on hand to unleash an unstoppable volley.
Arsenal should have taken the lead in the 64th minute, but Ainsley Maitland-Niles was denied by the hand of Timo Horn when trying to round the keeper.
He could do nothing soon after, though, as Sanchez cut in from the left wing and gradually worked an opening to unfurl a wonderful curler into the corner from 20 yards.
The visitors responded well, with Cordoba offering a reminder of his threat when forcing Ospina into action.
But, after Sanchez went close again, Arsenal wrapped up the points when Bellerin slid home on the rebound after Walcott's effort was saved.
Key Opta stats:
- This was Arsenal’s first European match outside of the Champions League (incl. qualifiers) for the first time since May 2000 – 17 years and 120 days ago.
- Arsene Wenger has now registered a win over 57 different clubs during his tenure as Arsenal manager (from 64 different teams faced).
- Alexis Sanchez scored his first ever goal in the UEFA Europa League, in what was his 10th appearance in the competition (9 for Udinese, 1 for Arsenal).
- Sead Kolasinac has now had a hand in four goals (two goals, two assists) in five appearances for Arsenal (incl. Community Shield).
- Kolasinac’s goal was the 200th scored at home in European competition under Arsene Wenger – totals now stand at 125 goals at the Emirates, 69 goals at Highbury & 8 goals at Wembley.