Leeds United forward Raphinha had a goal disallowed by the VAR early before netting the opener in the 28th minute, with new Aston Villa signing Coutinho adding a second on 62 minutes for his first international goal since 2020.
Brazil added two more in the dying minutes as Ajax forward Antony curled in, before Newcastle United addition Bruno Guimaraes laid off for Rodrygo to tap home.
The victory means Selecao, who have already clinched their spot at Qatar 2022, are unbeaten in 15 qualifiers and remain four points clear of rival Argentina at the top of the CONMEBOL standings.
Brazil has also won seven out of seven qualifiers on home soil, netting 18 goals and conceding only once, while Paraguay officially cannot qualify for Qatar 2022 due to the defeat.
Raphinha thought he had opened the scoring in the second minute but after a lengthy VAR review had his strike ruled out for handball.
The Leeds man would not be denied when he expertly controlled Marquinhos' pass, fired in low at the near post for 1-0.
Vinicius Junior should have doubled Brazil's advantage prior to half-time when in one on one but his heavy touch allowed Paraguay goalkeeper Antoni Silva to clear.
Silva made a fine save early in the second half from Thiago Silva's header while Lucas Paqueta's 56th-minute close-range effort went over the bar after a sublime pass from Coutinho.
Coutinho finally added the second when afforded too much space as he lashed into the top corner from outside the box in the 62nd minute.
Antony bent home the third off the post in the 86th minute, with Guimaraes cutting back for Rodrygo's 88th-minute tap-in.