The victory gave Tite his eighth win in eight games as coach and lifted leaders Brazil to 30 points in the South American qualifying group, a tally that has been more than enough to guarantee qualification in previous campaigns.
"We work hard every day and so this isn't an accident," Paulinho said of the three points and three goals, his first professional hat-trick.
"We played a great game and got a great win. We knew how difficult it would be here. We went behind, but we kept our concentration and we had the coolness to go after a result.
"Now we need to keep it up and I am sure this team has a lot more to offer."
The five-times World Cup winners led second-placed Uruguay by four points before the game but it was the weakened home side that took the lead after eight minutes thanks to a penalty from Edinson Cavani.
Marcelo tried to chest down the ball to his keeper but Cavani nipped in to intercept and was pulled down by Alisson. The Paris St. Germain striker got up to rifle the ball home low to Alisson's right.
It was the first time that Brazil had gone behind since Tite took over as coach last summer and it only took them 10 minutes to show they would not be bowed.
Neymar laid the ball off to Paulinho in midfield and the former Tottenham midfielder hammered home a spectacular right-foot shot from 30 yards out.
Read the full article on eurosport.co.uk: Paulinho hat-trick keeps Brazil on road to Russia