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.
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.