He became the first manager since Sir Matt Busby to win his fourth straight opening game as United manager with a routine 2-0 victory against Newcastle at St. James' Park.
However, the visitors found the net after 64 minutes and everything was much easier after that, with Rashford confirming the win with 10 minutes to play.
The game remained goalless until Lukaku's introduction and the Belgium striker prodded home with his first touch after Martin Dubravka spilled Rashford's 64th-minute free-kick.
Newcastle left themselves exposed for Lukaku and fellow substitute Alexis Sanchez to give Rashford a simple finish and, in stoppage time, Pogba rounded Dubravka on another counter-attack but fired into the side netting.
The result caps a superb run of form for Man United since the sacking of Jose Mourinho. Solskjaer couldn't have done any more. They started the new year having conceded 27 goals in their first 20 games - a better defensive record than both Manchester United and Arsenal.
Closing down the Frenchman in the 72nd minute at St James' Park, the England global lept in on the ex-Juventus midfielder, with his right boot halfway up Pogba's leg.
The fleet-footed Ghanaian quickly got another attempt on goal as United wobbled, with Phil Jones looking most likely to falter.
Rafael Benitez's side have only scored four second-half goals in the Premier League this season and did not pose the same offensive problems to United after the break.
"Newcastle with a bit more quality would have scored goals".
And the Old Trafford hero has clarified why he had an issue with Pogba's timing.
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