On a night when Vargas made the difference for his side once again, the forward had the first chance to open the scoring, but his shot was blocked by Christian Cueva.
Peru came closest to scoring in the first half though when Jefferson Farfan's header hit the post after nine minutes.
They continued to threaten the Chilean defence, and Carlos Lobaton was next to come close to giving Peru the lead, but he hit the side-netting.
Chile ramped it up a notch following Zambrano's red card, and Jorge Valdivia curled the ball wide of the target on the half-hour mark.
The lead belonged to Chile in the 43rd minute when Vargas tapped in from a rebound after Alexis Sanchez's inviting cross hit the post.
Shortly after the restart, Vargas thought he had scored his second goal of the match when he volleyed into the corner of the net, but the goal was ruled out for offside.
Peru managed to get back on level terms when Gary Medel could only head into his own net while attempting to clear a dangerous cross.
However, they were only level for five minutes as Vargas struck once again, unleashing a strike from 25 yards to leave Pedro Gallese helpless.
Vargas had the chance to complete his hat-trick when he found the space to meet an Arturo Vidal cross, but he could only send a header over the crossbar, and Vidal was also denied later on when his volley was pushed away by Gallese.
Despite the late miss, Vargas remained the hero for the hosts, who will meet either Argentina or Paraguay in the final as they look to win the tournament for the first time.