The Chilean's goal rounded off an extraordinary comeback from the Red Devils, who scored three times in the last twenty minutes.
United had started the game incredibly poorly, and this was shown when Kenedy put Newcastle in front after just 7 minutes.
The Brazilian was sent into an ancre of space by Ayoze Perez's excellent through ball, before curling a great finish past a helpless David De Gea.
United responded in the worst possible way, when three minutes later Yoshinori Muto doubled Newcastle's lead.
The Japanese international collected the ball in the penalty area, before showing great strength to shrug off Ashley Young before smashing the ball past De Gea from close range.
6 October 2018
Mourinho, who was reportedly in line to be fired no matter the result of this game, made an immediate change, sensationally substituting off Eric Bailly in favour of Juan Mata after just 20 minutes. The manager hugged Bailly as he left the pitch, seemingly making it clear that the change was purely tactical.
Two minutes later, Marcus Rashford missed an incredible chance to put United back in the game.
Romelu Lukaku curled in an inviting corss, and the English youngster could only direct his header wide, when he should have scored.
It was David De Gea who was the busiest of the two goalkeepers before half-time.
The Spaniard had to make a stunning reaction save when Muto directed his free header towards the United net.
At half-time, Mourinho and his players were booed off the pitch, two goals down to a team that had not won all season.
6 October 2018
United came out after the interval a new team, full of the kind of purpose that they had been sorely lacking.
Despite this, it looked for a while as though it just wouldn't be their day.
In the 51st minute, Dubravka was called into action to make a fine save from a deflected effort from Paul Pogba, who was excellent in the second period.
As he pushed the ball to Nemanja Matic, the Serb had an empty goal to aim at from six yards out, but he somehow managed to smash the ball over the bar.
It was an unforgivable miss, and few would have been more relieved to see United complete their comeback than Matic.
Said comeback began in earnest in the 70th minute, when Juan Mata scored a superb free-kick.
After Mo Diame was booked for tripping Anthony Martial on the edge of the box, Mata stepped up and beat the wall with an inch-perfect curling strike.
Newcastle keeper Dubravka made several good saves in the game, and the pick of the bunch came in the 75th minute when he denied Chris Smalling from just a few yards out.
Alas, his heroics were quickly forgotten, as United equalised a minute later through Anthony Martial.
The Frenchman played a scintillating one-two with countryman Pogba on the edge of the box, before tucking the ball in at the near post.
6 October 2018
United continued to press, far from satisfied with the prospect of a draw.
The efforts were rewarded in the 90th minute, when Alexis Sanchez scored a winner.
Ashley Young swung a cross into the box, and Sanchez buried a header, prompting jubilant celebrations at Old Trafford.
It's hard to see how Mourinho's sacking could be justified in the wake of that result - two of his substitutes scored, and his half-time speech appeared to have a huge effect on the team.
The result leaves United in 8th, while Newcastle languish in 19th with just two points.