Vargas scored a fine second goal from 25 yards out to take Chile through to the finals.
Peru played with 10 men for most of the game after Carlos Zambrano got sent off in the 21st minute for a knee in the back of Aranguiz.
Referee Jose Argote saw that as a red card offence.
The Peruvian sided were of the opinion that it was merely an unfortunate follow through from a clearance.
It gave Chile the edge that ultimately saw them through to the finals.
The Copa America is 99 years old and Chile have never won the trophy in all that long period of time.
They will play the winner of the Argentina – Paraguay semi final .
Argentina and Paraguay on the other hand have both been winners of the Cup in the past.
So maybe we should put our money on Chile because they will be all fired up to make history.
And a Chile on fire might prove too hot to handle.