The Belgian striker was joined on the scoresheet by Alexis Sanchez, for just the second time in his 11 United outings, in a routine 2-0 win over strugglers Swansea.
Mourinho’s players responded in style to the manager’s very public criticism of their efforts in the FA Cup victory over Brighton two weeks ago.
The United boss had accused his players of lacking “personality, class and desire” on that occasion.
However, with England international Jesse Lingard in magnificent form and having a hand in both goals, United had settled this game inside the opening 20 minutes.
“The first half was perfect,” said Mourinho. “One of the best halves we have played here.
“They (Swansea) didn’t cross the halfway line, they didn’t have one shot.
“We were so strong, we had lots of movement, lots of passing, we arrived in many dangerous positions, scored two, should have had at least one more.”
Lukaku’s 100th goal came after just five minutes as Lingard picked out Sanchez in the Swansea area who squared for Lukaku to score from 12 yards, via a deflection off Alfie Mawson.
“I’m really happy to achieve that milestone,” said Lukaku.
“It is a dream come true. I’m really happy to achieve that in a league I’ve wanted to play in since I was six years old.”
Just 15 minutes later, the points were as good as decided when Lingard collected the ball just inside Swansea territory and threaded through a magnificent pass for Sanchez to race on and deliver an unstoppable finish from the edge of the area.
Mourinho’s close friend Carlos Carvalhal, the Swansea manager, reshaped his team at the interval and brought on Tammy Abraham and Tom Carroll, prompting a very different second half.
– ‘Fighting for the title’ –
Still, the only moment of concern for David De Gea came on the hour when the Spanish keeper made two excellent, one-handed diving saves in quick succession from Abraham to maintain the two-goal cushion.
As United coasted to victory, Paul Pogba, handed a start for just the fourth time in United’s last 10 games, grew in influence and delivered two superb chipped passes that might have led to a third United goal.
But Juan Mata volleyed over spectacularly on the turn and Lukaku, having controlled Pogba’s pass on his chest, saw his shot blocked from six yards by Lukasz Fabianski.
Like Pogba, Sanchez’s form has also come under close scrutiny since his high-profile transfer to United but, as with his French team mate, the Chilean could be pleased with his afternoon’s endeavours.
“The team played very well in the first-half, so Alexis played well,” said Mourinho.
“But I think everybody played really well in the first half. Second-half I think Alexis was one of the guys who paid the price of the international week, playing two matches in three days.”
Mourinho pointed to that fatigue from last week’s internationals as one reason for his team, collectively, being less dominant in the second half.
However, with his club second in the table and facing an FA Cup semi-final with Tottenham later this month, the manager remained upbeat.
“Last season we won titles but finished sixth in the league,” he said.
“We want to finish second this year and have 10 points more than last season, more goals scored, less goals conceded, but there is a club (Manchester City) which is making it practically impossible to follow.
“In other leagues we would be fighting for the title.
“We are having a positive season and we still have the FA Cup to come.”
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