Uruguay, who were without Luis Suarez after the forward's positive coronavirus test, hit the crossbar twice in the first half before their chances took a further hit when Edinson Cavani was sent off in the 71st minute.
The result extended Brazil's unbeaten run against Uruguay to 11 matches.
While Brazil made a bright start, it was Uruguay who went closest to an early opener, Darwin Nunez powering an effort onto the crossbar from inside the area after cutting inside from the left in the fifth minute.
After a relatively even opening, Brazil struck twice in the 11 minutes before half-time through Arthur and Richarlison.
Arthur opened the scoring with his first international goal, the midfielder receiving a pass from Gabriel Jesus before seeing his 20-yard effort take a huge deflection and wrongfoot goalkeeper Martin Campana.
Roberto Firmino squandered a great chance two minutes later when he was denied by Campana, but Brazil would double their lead through Richarlison.
A short corner led to an unmarked Richarlison getting on the end of a Renan Lodi cross to head in and make it 2-0.
There was still time for Uruguay to be denied by the woodwork again to finish the half, Diego Godin's header hitting the crossbar after Nicolas De La Cruz's set-piece.
After few chances to begin the second half, Uruguay's comeback chances were dealt a blow in the 71st minute, Cavani having a yellow card for a challenge on Richarlison upgraded to a red following a VAR check.
Just as Martin Caceres thought he had given the hosts hope with a goal shortly after, it was correctly ruled out for offside, Uruguay unable to find a way back into the contest.
What does it mean? Brazil stay perfect
In what is a grueling qualifying campaign, Brazil have made a dream start with four wins from four. Tite's men finished top of the 2018 standings with 12 wins, and they are on track for another dominant campaign.
No Neymar, few problems for Brazil
Without their star forward due to a thigh injury, Brazil still managed back-to-back wins to continue their perfect start to qualifying. However, they missed the Paris Saint-Germain star's spark in Montevideo, creating few chances but making the most of those they had to claim three points.
Uruguay still can't find a way against Brazil
The loss extended Uruguay's winless run against Brazil to 11 games, with their last victory in meetings between the nations coming in 2001. It could have been different with some luck after Nunez and Godin hit the crossbar in the first half and Caceres had an effort ruled out in the second.
Brazil and Uruguay continue their qualifying campaigns in March next year. Tite's men will face Colombia and Argentina, while Uruguay meet Lionel Scaloni's side and Bolivia.