Hosts Paraguay, who had knocked the Selecao out of the Copa America last year, took the lead as the ball fell to an unmarked Dario Lezcano, who fired home five minutes before the break.
And just three minutes into the second half Paraguay doubled their lead as Edgar Benitez sneaked ahead of marker Dani Alvez to send the home fans into raptures.
Dunga’s men rallied however, as Ricardo Oliveira pulled one back with 11 minutes to go before Alves atoned for his earlier error, cutting inside from the right before firing home in the second minute of stoppage time to secure a point for his side.
It was Brazil’s second draw in succession, leaving them sixth on the South American World Cup qualifying table after six games, with only the top four guaranteed progression to Russia 2018.
Elsewhere, Argentina secured a routine 2-0 win over Bolivia, with right-back Gabriel Mercado opening the scoring on 20 minutes as Lionel Messi converted a penalty 10 minutes later to secure the win.
In Montevideo, Edinson Cavani’s 53rd minute goal secured Uruguay a 1-0 win over Peru to go joint-top of South America’s qualifying table alongside Ecuador, who went down 3-1 to rivals Colombia.
South American World Cup qualifying table:
Tuesday night’s South American World Cup qualifying results:
Colombia 3 – 1 Ecuador
Uruguay 1 – 0 Peru
Argentina 2 – 0 Bolivia
Venezuela 1 – 4 Chile
Paraguay 2 – 2 Brazil