Machis got Venezuela off to a perfect start by powering in a header in the second minute, scoring their first goal of the tournament after back-to-back goalless draws against Peru and hosts Brazil.
Machis scored a spectacular goal to put his side further at ease early in the second half, bursting down the left wing on the counter-attack and holding off three defenders before cutting inside to lash the ball into the net from just inside the area.
Neymar guides Brazil to winning start at Copa America
Bolivia pulled a goal back in the 83rd minute through Leonel Justiniano but their hopes of grabbing an equaliser proved short-lived as Josef Martinez leapt to head in Venezuela's third three minutes later.
Venezuela finished second in Group A on five points, Brazil came first with seven, with Peru third on four and Bolivia last without a point.
Venezuela have qualified for the quarter-finals in four of their last five appearances in the Copa America, with their best effort coming in 2011 when they reached the semi-finals but lost to Paraguay on penalties after a 0-0 draw.
They will meet the Group B runners-up in the last eight, which could be Argentina, Qatar or Paraguay, who play their final games on Sunday.
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World Cup Qualification CONMEBOL
Firmino scores as Brazil labour to win over Venezuela