The victory consolidated Chile's hold on fourth place in the South American group with 21 points from 13 matches, behind Ecuador on goal difference after the Ecuadoreans were earlier held 1-1 at home by Argentina.
The top four teams qualify for the 2014 finals in Brazil and the fifth goes into a play-off with an Asian side.
Striker Eduardo Vargas scored in Chile's first dangerous approach from a cross by Eugenio Mena in the 16th minute.
The Chile fans were still celebrating when Sanchez doubled the advantage two minutes later with a header from the rebound of a shot by midfielder Arturo Vidal that hit the bar.
It was Sanchez's first international goals in almost two years. His last goal was in July 2011 at the Copa America in Argentina.
Pizarro, who had turned his back on the national team over other players' indiscipline and then refused several previous recalls, was important as playmaker, generating space and delivering deep crosses to the forwards.
Bolivia pulled one back when striker Marcelo Martins scored after the half hour mark, but the visitors never troubled Chile goalkeeper Claudio Bravo again in the first half.
Chile stepped back a few metres in the second half and allowed Bolivia to create some chances but they regained prominence and justified the victory.
Pizarro almost scored near the end with a long distance effort before Vidal headed a Jean Beausejour cross home in added time to seal the result.
- Sports & Recreation
- Eduardo Vargas
- Eugenio Mena