Oswaldo Vizcarrondo gave the Venezuelans a surprise lead in the 35th minute at the Estadio del Bicentenario. Claudio Borghi's side raised their game and grabbed a deserved equaliser through Humberto Suazo, but Gabriel Cichero capitalised on a fumble from Chile goalkeeper Claudio Bravo nine minutes from time to nick the winner.
Gary Medel added to Chile's woes when he was sent off two minutes later and, although Tomas Rincon's stoppage-time dismissal evened up the personnel, there was no time for a leveller on the scoresheet. Venezuela keeper Renny Vega was in inspired form throughout, not that he had too much to do in the first half.
Vizcarrondo puts Venezuela ahead
He made a comfortable early save from an Alexis Sanchez header before the deadlock was broken at the other end, centre-back Vizcarrondo flicking a fine header past Bravo from Juan Arango's free-kick.
Vega fisted a Pablo Contreras header to safety to preserve his side's lead at the interval. The half-time introduction of Jorge Valdivia had a positive effect on Chile, who looked a different team at the start of the second period.
Sanchez had a header cleared off the line by Cichero in the 54th minute and Suazo lashed a fierce shot against the bar moments later. Palmeiras midfielder Valdivia unleashed a long-range effort in the 58th minute which left Vega rooted to the spot but he too was denied by the woodwork.
La Roja continued to press but Vega was in the right place to keep out a Medel header and then a Sanchez strike after the highly-rated Udinese winger had weaved his way into a shooting position. Chile did not have to wait too much longer for the equaliser, though. Sanchez's cutback found an unmarked Suazo, whose shot went in off the bar.
Cichero clinches victory
There looked to be only one winner at that stage but Venezuela, unbeaten in the tournament so far, once again proved they should not be written off in the 81st minute. Bravo failed to hold onto Arango's free-kick and Cichero was on hand to prod home the rebound.
It got worse for Chile two minutes later, when Medel's handball saw him sent off for a second bookable offence. Vega pulled off a brilliant double save to keep out a Suazo blast and then Arturo Vidal's follow-up six minutes from the end.
Rincon was shown a straight red card deep in stoppage time for a cynical foul on Valdivia, but that hardly dampened Venezuela's celebrations as they secured a last-four date with Paraguay in Mendoza on Wednesday.