With reports swirling that Mourinho could be sacked regardless of the result in Saturday's late kick-off, the manager was typically bold in giving the star forward a watching brief.
Muto went close to a third for Newcastle with a header which De Gea did well to keep out with a reflex save.
But Pogba's early shot was only parried by Martin Dubravka, the ball falling to Nemanja Matic who somehow cleared the open goal from six yards with a miss which summed up United's woes.
The Red Devils piled-up the pressure after the break, and Juan Mata swept home a world-class free-kick with 20 minutes left.
Mourinho refused to name names when pushed on who else was at fault for United's form but did say: "The same people that were to blame with the fantastic season of last season".More news: Chris Evans bids farewell to Captain America
"At half time we were losing 2-0 and the fans were magnificent to the team".
As usual, Neville was working for Sky Sports during Brighton's 1-0 win over West Ham and after the game, Kelly Cates asked the former Manchester United defender if sacking Mourinho would be the right decision from the United board.
It was a day where he could be happy with his substitutions though with Mata getting the first and Sanchez getting the victor whilst the decision to move Paul Pogba deeper certainly worked as the Frenchman ran the game in the second half.
But with his future now a matter of daily discussion and headlines suggesting his time as manager is running out, Mourinho wants Woodward to dismiss all reports of his job being on the line.More news: UK's May aims to gain Conservative control after storm Boris
Manchester United came from two goals down to win 3-2 tonight.
The centre-back watched Kenedy run past him for Newcastle's first goal and generally looked all at sea until Mourinho substituted him in the 19th minute in order to bring on Mata.
Mourinho responded to the criticism coming his way by claiming United overachieved in finishing second last season, 19 points behind champions Manchester City, adding he always expected this campaign to be more hard.
It comes after a week in which Mourinho said some players "care more than others" in the build-up to the goalless Champions League draw with Valencia.More news: Chicago police officer jailed after guilty verdicts