The Red Devils were looking to extend their winning run to four games under interim Manchester United manager.
Manchester United struggled to make a breakthrough against a defensive Newcastle side at St James’ Park in the opening 63 minutes.
Solskjaer opted to bring on Romelu Lukaku and Alexis Sanchez for Anthony Martial and Juan Mata with 26 minutes left to play.
And Lukaku had an immediate impact with the opener after he pounced on the loose ball to fire Manchester United into a narrow lead at St James’ Park.
Sanchez provided an assist for Marcus Rashford to double the away side’s lead with 10 minutes left to play.
Solskjaer has a 100 per cent as Manchester United manager after he replaced Jose Mourinho last month.
Former Spurs striker Lineker heaped praise on Solskjaer for his inspired second-half substitutions.
Lineker wrote on Twitter: “Solskjaer’s a master-coach. What a substitution.
On Sanchez’s assist, the Match Of The Day host added:
“Who would ever have thought? Sanchez can still play.”
Manchester United moved to within six points of fourth-placed Chelsea FC after the Blues were held to a frustrating 0-0 draw with Southampton on Wednesday night.
The Red Devils will take on Tottenham at Wembley in their next Premier League game on Sunday 13 January.
Manchester United will host Reading in the FA Cup third round at Old Trafford next Saturday.
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