A Three Lions line-up which included debutants Fraser Forster, Adam Lallana and Jay Rodriguez made a sluggish start and fell behind inside seven minutes on Friday night.
As the hosts failed to clear their lines, Eugenio Mena sent over a teasing delivery from the left and in-form Sanchez got across Leighton Baines to divert a stooping header into the bottom corner.
The Barcelona forward ended any hope England had of getting back into the game in the fourth minute of second-half stoppage-time as he was freed in space and delicately dinked the ball over the onrushing Forster.
James Milner drilled an early cross in to the Chile box that was cleared off the line, as England tried to get on the front foot, but the Wembley crowd were left scratching their heads moments later.
Chile surged forward on the counter, Gary Cahill put his body on the line to block a shot from Eduardo Vargas but the danger had not passed.
The visitors moved the ball out to Mena on the left, Cahill missed the full-back's cross and Sanchez sneaked in front of Baines to head beyond Forster.
Jorge Sampaoli rejoiced while Roy Hodgson sat despondent.
Phil Jones frayed the England manager's nerves further with a pass that Chile capitalised on. Jean Beausejour gained a yard on his marker but Forster saved well.
Frank Lampard raised spirits briefly with a fierce long-range free-kick.
Claudio Bravo's theatrical save made the shot look better than it was, however, and the momentary lift the crowd experienced soon made way for more groans.
England could not get Chile off the ball. Gary Medel in particular was having a superb game, passing the ball out of danger through his wing-backs whenever England applied pressure.
Wayne Rooney was the next person to yell at his own team-mates.
Defence remained England's weakest point. Cahill somehow managed to lose the 5ft 7in Medel, but he put his free header over.
Chile had one over on the break on the half hour, but Forster came out to usher Beausejour wide.
Rodriguez's limp shot trickled in to Bravo's arms, summing up England's first half.
England were all at sea just before the break, with Sanchez breaking through twice, although Lallana pierced the Chile defence only to be thwarted with a last-ditch tackle.
A few boos rang out at half-time.
England's issues continued after the restart. Baines failed to find James Milner with a simple 10-metre pass from a corner, which did not go down well with the home fans.
The biggest cheer of the night came when Andros Townsend came on for Rodriguez on the hour.
The Tottenham winger had an immediate impact, finding Jack Wilshere, who was fouled on the edge of the box by Medel.
The home crowd held their breath as Baines stepped up to take the free-kick, but he found the wall.
Jermain Defoe, Tom Cleverley, Ross Barkley and Jordan Henderson came on, but they had little impact. Chile were still running the show. Even with 10 England players camped out in their half, they still passed the ball without fear as their fans chanted "Ole!".
And Sanchez hammered the final nail in to England's coffin in injury time when he lifted the ball over Forster after a mix-up at the back.
|0||1st Half Goals||1|
|5||Shots on Target||4|
|4||Shots off Target||1|
|42||1st Half Poss.||58|
|41.5||2nd Half Poss.||58.5|