Fly-half Sanchez scored five and kicked 15 points to become his country's top scorer at a World Cup, adding to tries by Juan Martin Gonzalez (2), Agustin Creevy, Martin Bogado, Rodrigo Isgro, Ignacio Ruiz and Santiago Carreras to put Argentina in second place on nine points.
Argentina lead third-placed Japan on points difference ahead of their meeting next week with a quarter-final spot at stake while Chile exit the tournament bottom of the group with zero points despite scoring a late try through Tomas Dussaillant. Pool D leaders England have qualified in top spot.
"It was very special for me. My family are here, 100 caps. I am very happy," Sanchez said.
Despite lapses in concentration, Argentina were always in control and coach Michael Cheika was looking forward to the Japan game.
"They are a great team, they are quarter-finalists from the last World Cup and we're not so we're very hungry to be in that position," Cheika said.
His Chile counterpart Pablo Lemoine was grateful for the World Cup experience as the South American country were taking part for the first time.
"It was an amazing month here. This Rugby World Cup has given us a lot and put Chilean rugby on a different path. We expected the World Cup to help Chilean rugby and we did it," he said.
At Nantes' La Beaujoire stadium, Sanchez, the team's all-time top scorer with 872 points, put Argentina ahead with an early converted try, diving over after a nice dummy.
He added a penalty before number eight Gonzalez crossed from a maul as did hooker Creevy for the Pumas' third midway through the opening half.
Rodrigo Isgro's yellow card for a high tackle on Rodrigo Fernandez slowed Argentina's progression and no other points were scored before halftime.
Having nothing to lose, Chile came back from the dressing room with a very offensive mindset but were caught cold when Bogado beat Inaki Ayarza's tackle for Argentina's fourth try.
The crowd went wild when Chile's Augusto Bohme touched down after a clever lineout, only for the try to be ruled out for a forward pass.
Argentina were ruthless, Isgro adding another try as he dotted down under the posts before Gonzalez claimed a double.
Dussaillant finally put Chile on the scoreboard to send their many fans wild, but they faced a fierce backlash as Ruiz and Carreras crossed to complete Argentina's crushing win.
