The Chilean striker lost possession of the ball by the left touchline with the game still goalless, allowing Dinamo to start a long break towards the Arsenal goal.
But Sanchez, determined to right his mistake, chased back deep into his own half, dispossessed his opponent and recovered the ball to set an Arsenal attack in play.
After he passed the ball on, he went back to the touchline, and threw the gloves he had been wearing from the start on a chilly night into the crowd.
The gloves, were literally off. Sanchez was firing on all cylinders and a few minutes later he ran 50 metres towards the Dinamo area to set up Arsenal's first goal for Mesut Ozil.
He then scored two himself to take his tally this season to nine in all competitions, and afterwards won the praise of both his manager Arsene Wenger and Dinamo's manager Zoran Mamic.
Wenger was thinking of substituting him after Arsenal went 3-0 up but had reporters laughing when he said, tongue-in-cheek: "I didn't take him off because a break makes him tired.
"But I would have loved to have taken him off really, but the compromise was to leave him in the centre where he can save a little energy, I tried to compromise a little bit.
"He is just such an important player because at the moment all we have as strikers are Olivier Giroud and Sanchez, and Giroud had a little problem with his ankle over the weekend so I decided to give him a breather.
"So I took him off and Hector Bellerin off, because he had a slight groin problem, so I couldn't take Sanchez off."
Sanchez left his mark with a touch-in for his first goal, Arsenal's second, after 33 minutes and by scoring a delightful goal to put his side 3-0 up when he left Dinamo keeper Eduardo stranded and scored from a tight angle after 69 minutes.
Dinamo coach Mamic said: "Angelo Henriquez plays with Sanchez for Chile and so we knew all about him, but what can you do with a player like that -- he is one of the best strikers in the world."
(Reporting by Mike Collett; Editing by Ken Ferris)
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