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Raphinha made it 2-0 after 18 minutes when he bundled home a parried shot from close range and then made it 3-0 after 58 minutes, completing a superb counter-attack with an angled shot.
Luis Suarez scored a consolation goal for Uruguay with a 77th minute free kick before Gabriel Barbosa restored Brazil's three-goal cushion with a header seven minutes from time.
"This couldn't be more memorable for me," Raphinha said. "This is me fulfilling my childhood dream. It's so gratifying to score.
"It's going to be very difficult to forget this night."
Both Neymar and Raphinha could have scored more, with Uruguayan keeper Fernando Muslera thwarting both in quick succession early in the second half.
It was a measure of Brazil's superiority that Muslera was Uruguay's best player on a poor night for the visitors, who have now won only two of their last nine qualifiers.
The top four qualify automatically for Qatar 2022 and the fifth-placed side goes into an inter-regional playoff.
Also on Thursday, Chile beat Venezuela 3-0 to record their second successive win. Erick Pulgar scored twice in the first half, both off Alexis Sanchez assists, and Ben Brereton made it 3-0 17 minutes from time to lift Chile onto 13 points in sixth place.
Venezuela, who have lost nine of 12 qualifiers, are bottom of the group on seven points, four adrift of Peru.