The Gunners were 2-0 up at half-time thanks to goals from William Saliba and Gabriel Jesus before Vieira got a hold of the ball in the 49th minute. The 22-year-old had the freedom in west London to unleash a vicious strike from outside the area and his effort crashed in off the post.
Vieira's strike all but sealed the three points for Arsenal, with a victory in the London derby sending them back to the top of the Premier League.
The Portugal U21 international was handed his first start for the club due to Martin Odegaard's injury, as he slotted into the attacking midfield role.
The playmaker took full advantage of his opportunity and scored a goal that Gunners fans won't forget in a hurry.
Vieira joined the club from FC Porto in a £31.5 million summer move (Transfermarkt). He was widely considered to be a real coup for Mikel Arteta's side as he was the top assist provider in Liga Portugal last season with 14 assists.
Following his terrific strike, the Gunners fans took to Twitter to praise their new superstar, who they have high expectations for:
Fabio Vieira told to "toughen up" by former Arsenal striker
After the creative Portuguese midfielder started the Gunners' Europa League tie against FC Zurich, former Arsenal striker Kevin Campbell appeared unimpressed.
Vieira didn't contribute much to his team's 2-1 victory and Campbell had some advice for the youngster, who is new to English football. The former Gunners striker told The Highbury Squad (as per The Express):
"It was his first start and it was always going to be a tough one. Look, the opposition weren’t great. And you know what they are going to do about it? Is make up for it with grit and that’s what they did. I thought Vieira... we saw flashes of quality. The one quality we did see was him releasing Eddie [Nkeitah] down the left-hand side for the goal. Showed good touches."
"They [Zurich] had a bit more grit in midfield and that’s what he has to learn. He is playing for Arsenal now. When Arsenal turn up, you are going to get the best of everybody else."
Vieira certainly has plenty of potential. If Odegaard's injury becomes a problem for Arteta, he certainly appears able to fit into the Norwegian international's shoes.