The Chilean, who had been rumoured to have had his own falling out with Jose Mourinho this week struck in the 90th minute to break Newcastle's hearts.
The diminutive attacker rose highest to convert Ashley Young's cross from the right and send the home fans wild.
Sanchez has received a lot of criticism for his recent form, but showed he is a man for the big moment as he scored the winner.
Goals from Anthony Martial and Juan Mata had brought United level after Yoshinori Muto and Kenedy had given Newcastle a 2-0 lead early on.