Goals in each half from Paris Saint-Germain star Thiago Silva and Bundesliga-based striker Roberto Firmino clinched a win which ensured Brazil qualified for the last eight on top of Group C.
Venezuela's goal came from Rayo Vallecano striker Nicolas Fedor in the 84th minute.
Silva - who earlier celebrated finding the net with a dedication to Neymar - praised Brazil's team effort.
"The best thing today is we had a very cohesive team," he said. "Football is played this way -- as a team.
Brazil will now face Group B runners-up Paraguay in the quarter-finals on Saturday.
"It's going to be a tough match," said Silva of the 2011 finalists, who knocked Brazil out four years ago.
"Any team here is hard. Paraguay got to the last Copa America final and got there on merit, beating us along the way.
"Beating them on Saturday will have a special meaning."
Defeat to Venezuela on Sunday would have seen the five-time world champions making a humiliating first-round exit from the South American showpiece but that outcome never looked likely as Brazil dominated the start.
Brazil coach Dunga had opted to replace Neymar -- looking down from the stands at Santiago's Estadio Monumental -- with Santos striker Robinho while the captain's armband was passed to defender Miranda.
With Colombia being held to a 0-0 draw in the earlier Group C game, Brazil headed into the match comfortable in the knowledge that a point would be good enough.
The breakthrough came after only nine minutes.
Robinho flighted a corner from the right into the heart of the penalty area and Silva was on hand to sidefoot a sweetly struck volley past goalkeeper Alain Baroja, who failed to react in time as the ball flew into the roof of the net.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
