The Inter Milan midfielder put the hosts ahead in the 20th minute by blasting an unstoppable 30-yard drive into the top-left corner of Pedro Gallese’s goal.
The 33-year-old struck again 15 minutes later by bundling home from close range after Felipe Mora’s header from the edge of the six-yard box deflected off Andre Carrillo.
The result marked Chile’s first win of the South American zone qualifiers following a draw with Colombia and a loss to Uruguay in their opening fixtures last month.
Peru have drawn one and lost two of their three games so far.
Earlier on Friday, Uruguay beat Colombia 3-0 in Barranquilla with goals from Edinson Cavani, Luis Suarez and Darwin Nunez.
He discussed the game after the final whistle, saying: “I am happy for the goals, but the most important thing is that the National team won at home.”
Vidal pushed the team forward, adding: “Now we have to focus on Venezuela. We know that all teams are very difficult to face, but we have to play at 100%. We cannot lose points as we did in the previous qualifying rounds. We must go to another World Cup.”
Vidal has made 10 appearances across all competitions so far this season for the Nerazzurri, for a total of 661 minutes. In that time, he has been a strong defensive midfielder for coach Antonio Conte.
The 33-year-old has made 118 appearances for Chile since his debut in 2007, scoring 31 goals and providing nine assists.
