Sanchez opened the scoring after just five minutes in the World Cup qualifier, curling in a stunning free kick to net his 37th goal in his 108 appearances.
Paredes grabbed his second of the game in the 22nd minute after being set up by Sanchez, who directed a header into his path from the back post.
West Brom's Salomon Rondon pulled one back for Venezuela after 62 minutes but it proved only a consolation goal.
The result means Chile now sit in fourth in the group, leapfrogging past Argentina, who lost 2-0 in Bolivia.
Hours after Lionel Messi was suspended by FIFA for four World Cup qualifying matches, his country struggled in the altitude of La Paz and heightened its risk of missing a spot at Russia 2018.
Argentina dropped from third to fifth place, remaining on 22 points in South American qualifying with four games to play and putting coach Edgardo Bauza under intense pressure to step aside.
South America has four direct spots at the World Cup, and the fifth-ranked team goes into an inter-continental playoff against the Oceania qualifying winner for another spot at Russia next year.
While Argentina struggled, Colombia had a 2-0 win at Ecuador, posting its first win in Quito in 20 years and ensuring it will end the round in second or third spot. Ecuador dropped out of the top five for the first time, slipping to sixth with 20 points.
The result at Quito opened the prospect of a possible early qualification for leaders Brazil, which has won seven straight and has 30 points from 13 matches in qualifying.
If the Brazilians beat seventh position Paraguay in Sao Paulo, they will have enough points to secure a top-five spot in qualifying.