Goals from Thiago Silva and Roberto Firmino set the Selecao on their way to all three points in Santiago, a result which knocked their opponents out and ensured Colombia also progressed to the last eight from Group C.
A diving header from Venezuela substitute Miku six minutes from time set up a tense and enthralling finale but no one could deny Brazil were good value for their win, even without their talisman Neymar.
The Selecao took the lead after nine minutes when poor Venezuelan defending allowed Thiago Silva to casually get on the end of a corner to power the ball into the net from 12 yards. Goalkeeper Alain Baroja could have done better but was left wildly exposed by his defenders.
Former Manchester City forward Robinho was charged with filling Neymar’s boots and he nearly doubled his side’s lead a few minutes later, sweeping a first time effort from the edge of the box just over the bar.
Chelsea full-back Filipe Luis then went close for Brazil, with his volley stinging the palms of Baroja. From the resulting corner Robinho and Thiago Silva tried their luck but both attempts were blocked.
Robinho seemed to be enjoying his evening back in the Brazilian starting line-up and he nearly set up Willian but the Chelsea forward’s effort from a tight angle was blocked by Baroja.
Venezuela made two changes at half time with Josef Martinez and Cesar Gonzalez coming on and they seemed to start the half with real attacking intent.
However, it was Dunga’s side who got the next goal. Willian eased past Rosales Roberto on the left hand side before delivering a cross with the outside of his boot into the path of Firmino who couldn’t miss from four yards.
Juan Arango went close to reducing Venezuela’s deficit shortly after but his dipping free kick was pushed over the bar by Brazilian goalkeeper Jefferson.
Thiago Silva then had to look alert to block Gonzalez’s effort from close range, with the Venezuelan substitute also going close moments later, firing just wide of Jefferson’s right hand post.
David Luiz nearly announced his introduction to the game from the Brazil bench in spectacular fashion but his acrobatic overhead kick was saved by Baroja.
Venezuela ensured a nervy final few minutes for Colombian fans when they pulled a goal back. Arango’s free kick from 20 yards was pushed on to the post by Jefferson but Miku was on hand with a diving header to give his side a glimmer of hope.
And the substitute nearly completed a remarkable comeback for Venezuela with the clock ticking down. Martinez found space on the left hand side to deliver a brilliant cross into the six yard box but the attacker just couldn’t reach the ball as it crossed the face of goal.
That result meant that Colombia’s earlier 0-0 draw with Peru was enough to see both sides advance to the last eight.
However, they face probably the toughest challenge in the competition with a quarter-final tie against Argentina to look forward to.
Hosts Chile will face Uruguay, Bolivia will meet Peru, while Brazil have a tie with Paraguay to prepare for.
That means that the Selecao could potentially meet arch-rivals Argentina in the semi-final.