The £34million summer signing from Porto has had a slow start to his Gunners career after suffering an injury in pre-season.
But he made up for lost time on his first Premier League start with a fine finish from the edge of the box to wrap up a 3-0 win in west London.
"I'm really happy, of course, to score my first goal with this club," the Portuguese midfielder told Arsenal.com.
"We've started this season really well and we need to keep doing this. "Everybody plays, everybody knows what they have to do on the pitch and we need to keep doing this." Arsenal were back at the scene of their dismal 2-0 opening-day defeat last season which pre-empted their worst start to a campaign for 67 years.
But they are a different animal this term and proved it with an organised, inventive display and three well-taken goals from William Saliba, Gabriel Jesus and Vieira. The Gunners took the lead in the 18th minute, Saliba's glancing header from Bukayo Saka's corner bouncing in off the inside of the far post. Ten minutes later Jesus doubled the lead with another header, this time from a neat chip into the box from Granit Xhaka, before Vieira's flourish put the seal on a clinical victory.
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