The Juventus midfielder's deflected effort opened the scoring in the 34th minute in Montevideo, where Richarlison doubled the lead and Edinson Cavani later saw red for the hosts on Tuesday.
Tite's men made it four wins from four to begin World Cup 2022 qualifying, while extending their unbeaten run against Uruguay to 11 games.
After scoring his first goal in Brazil colors, Arthur was delighted to contribute for his national team.
"I think it was essential to score this goal. For me, the most important thing is to play well and be able to help the team," he said.
"The goal was good to consolidate my performance and help our team. Professor Tite is always watching everyone."
Through four games, Brazil are two points clear of rivals Argentina in CONMEBOL qualifying.
Arthur said Tite's side were targeting top spot in the grueling qualifying campaign.
"Our goal is this [to win qualifying]. We are working hard in search of our goal," he said.
"We always have something to improve. We did not enter thinking that we are unbeaten because each game is different and difficult.
"We are on a good path, we trust the technical committee and they trust us. Now it is time to continue working and seeking this qualification for the World Cup."
Brazil started their campaign with wins over Bolivia (5-0) and Peru (4-2), but were challenged this month in victories against Venezuela (1-0) and Uruguay.
Tite said his side, whose next outings are against Colombia and Argentina in March, had to get used to different types of games.
"I feel that the team is consolidating, rolling, maturing, feeling the difficulties, reacting on top of the difficulties," he said.
"You don't dominate the game all the time. You have to control the opponent."