The visitors had become the first team to score twice in the first 10 minutes of a Premier League match at Old Trafford as Kenedy and Yoshinori Muto, with his first goal for the club, put them in control.
First-half substitute Juan Mata gave Manchester United hope with a 70th-minute free-kick and Anthony Martial then collected Paul Pogba’s backheel to equalise six minutes later.
In a dramatic finale Sanchez beat a crowd of players to head in Ashley Young’s cross and earn a dramatic victory for Jose Mourinho's side.
Man Utd move up to eighth place with the win, while Newcastle are 19th with two points this season.
Man Utd: 20 Oct v Chelsea (A)
Newcastle: 20 Oct v Brighton (H)