Carlos Zambrano's harsh sending off for a high tackle after 20 minutes was the second game in a row that Chile's rivals have been hit with controversial red cards.
The decision was a hard one to swallow for Peru, who in spite of being underdogs had started well in front of a capacity crowd at Santiago's National Stadium.
“I think Zambrano's expulsion was a bit tough,” Peru striker Paolo Guerrero told television cameras.
“I don't want to complain about the refereeing but there were a lot of unexpected decisions. If it had been 11 against 11 it would have been a different story.”
Chile's opponents in last week's quarter-final, Uruguay, were reduced to nine men in controversial fashion with Edinson Cavani and Jorge Fucile being sent off in Santiago.
Cavani's red card came after Chile defender Gonzalo Jara stuck his finger up the striker's backside and when he responded with the slightest of touches Jara fell to the ground theatrically, prompting the referee to send the Uruguayan off.
Chile got the decisive goal shortly after.
Jara later had a three-game ban for provoking Cavani cut to two by the governing body of South American football.
Peru refused to cave in after Zambrano's dismissal and matched their hosts in a pulsating first half.
But just when it looked like the teams would go in all square at half time Chile took the lead when striker Vargas poked the ball home from three yards after an Alexis Sanchez cross had come back off the post.
Television replays showed Vargas was marginally offside, but justice seemed to be done seconds into the second half when he had what looked like a legitimate goal chalked off for offside.
Peru came back into the game and equalised on the hour mark when Guerrero split the Chilean defence with a pass for Luis Advincula. He whipped in a cross from the right that Gary Medel turned into his own net.
Peru's lead lasted just four minutes, however, and again it was Vargas who did the damage as he picked up the ball in midfield and lashed home an unstoppable strike from 30 yards.
Chile, who have never won the Copa America in its 99-year existence, will play the winners of Tuesday's semi-final between Argentina and Paraguay. – Reuters
Original source: Chile into Copa America final