Talisman Neymar scored one and assisted another, adding a second for Tite’s side with a second-half penalty before setting up Gabriel Barbosa late on.
Paris St-Germain defender Marquinhos bundled in a 23rd-minute opener after Venezuela failed to clear a corner.
Nine-time winners Brazil won a first Copa America title in 12 years in 2019.
Twelve of Venezuela’s players and coaching staff tested positive for Covid-19 a day before their opening match in Group A, which also includes Colombia, Ecuador and Peru.
Colombia won their opener against Ecuador 1-0, with Edwin Cardona scoring the only goal of the game minutes before half-time from a cleverly-worked free-kick.
The goal was initially ruled out for offside but the video assistant referee (VAR) overturned the decision.
Everton forward Richarlison had a first-half goal disallowed for offside and Neymar missed from close range as Brazil initially struggled to make their dominance count.
Neymar scored his 67th international goal after Yohan Cumana fouled Danilo, but he missed another great chance to move closer to Pele’s national record of 77, shooting wide after breaking through the Venezuela defence in the closing stages.
The PSG forward then rounded goalkeeper Joel Graterol before squaring to substitute Barbosa for a tap-in.
The 47th edition of the Copa America – delayed a year because of the coronavirus outbreak – is taking place in Brazil, after Colombia and Argentina were stripped of the tournament.
The South American Football Confederation (Conmebol) removed Colombia as co-hosts in May amid anti-government protests and Argentina were later replaced because of rising Covid-19 cases in the country.