- Insider Notebook: Man United transfers special
Speaking after the match, Brazil captain Casemiro said his side deserved praise for their impressive performance.
"Without a doubt, we have to highlight the fact that we took this seriously," the Real Madrid midfielder said. "At no time did we try any funny stuff, we were always respectful.
"That's football, if you have the opportunity, then try and score more. We took this game 100% seriously."
Despite not getting his name on the scoresheet, Neymar -- who had been a doubt for the match -- produced some dazzling pieces of skill throughout.
Brazil overran Bolivia and could have scored more but for profligate finishing and decent goalkeeping.
Everton and Marquinhos both missed golden opportunities during the first three minutes but Marquinhos eventually broke the deadlock with a header after 16 minutes.
Firmino then added goals either side of half time before Carrasco's own Coutinho completed what was the perfect start for the home side.
The result takes Brazil to the top of the South American qualifying group after just one game, ahead of Colombia, who beat Venezuela 3-0; Uruguay, who needed a controversial late goal to overcome Chile 2-1 on Thursday; and Argentina, who beat Ecuador thanks to a Lionel Messi penalty.
Brazil now go to Lima to play Peru on Tuesday but Casemiro warned their latest triumph will count for nothing against the in-form Peruvians.
"I think there's always room for improvement, what's important is getting used to playing together," he added.
"We'll adapt better as we play more games. That's what is important. We deserve congratulations today. We were always looking for goals."