Bolivia had not won a World Cup qualifier away from home since 1993 but Brazil were still excellent, particularly in the first half, when they scored four of their five goals.
Neymar opened the scoring after just 10 minutes when he dispossessed Ronaldo Raldes on the halfway line and then worked a one-two with Gabriel Jesus, who left him with a simple tap in.
Philippe Coutinho doubled their lead 15 minutes later when he capitalised on great work from Giuliano and Dani Alves to poke home from close range.
Filipe Luis started the move for the third in his own half and after feeding Neymar, got the return pass and slotted the ball inside Carlos Lampe's near post.
Gabriel Jesus gave them a 4-0 lead two minutes before half time when he deftly chipped Neymar's pass over Lampe.
Substitute Roberto Firmino scored the fifth from a corner after 75 minutes, meaning Brazil stay in second place in the 10-team South American qualifying group.
The top four qualify automatically for Russia 2018 with the fifth place side playing the Oceania champions in an inter-continental showdown.
Uruguay maintained their place at the top of the group on 19 points, one ahead of Brazil with a 3-0 win over Venezuela.
Nicolas Lodeiro headed home the opener in 28 minutes and then Edinson Cavani doubled their lead just seconds after half time before adding a third 12 minutes from time.
Ecuador eased past Chile by the same scoreline with Antonio Valenzuela and Cristian Ramirez scoring in the first half before Felipe Caicedo made it three a minute into the second period to move into third on the standings on 16 points.
Copa America champions Chile are struggling with 11points from nine games.
Edwin Carmona gave Colombia a 1-0 win in Paraguay when he dinked home a lovely chip in injury time.
(Editing by Greg Stutchbury)
