But the away side grew into the game and started to put pressure on the Manchester United defence with some incisive football.
And the Saints could also have been awarded a penalty or two in the first-half.
The procession of wasted opportunities continued for United before the interval although Chris Smalling came close, with a header from a Young corner which flew just wide.
Andreas Pereira equalised in the 53rd minute after another powerful shot from way out, assisted by substitute Diogo Dalot.
After a lacklustre first-half display, United were now in an irrepressible mood and took the lead just six minutes later through Lukaku although Pereira was again instrumental in the goal.
We spoke about it at half-time and said get the ball in the box and play more forward because the Stretford End will suck it in for you.
A stunning effort to draw his side level nearly equalled the spectacle of Yan Valvery's opener for the visitors, before turning creator as he laid the ball into the path of Romelu Lukaku to score United's second.
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"We created a lot of chances in the opening 10 minutes but won the game".
The Manchester United boss told the BBC: "It was one of those games, it had everything. We'll take that as it comes". Those two strikes for them - absolute quality. He had a couple of crosses in the first half and his strike was fantastic.
"The belief is there, they have gone so long without losing games [domestically] and are raring to go".
"They've got to understand that this is the best time of their lives playing here". He has got quality in his passing crossing and shooting. "That's why we are turning grey".
After drawing 2-2 to Burnley, losing 2-0 to Paris Saint-Germain and drawing 0-0 to Liverpool in our last three home fixtures, I was beginining to think the Theatre of Dreams was cursed. "We are confident away from home, we can score goals and we are good at comebacks." he said.
"We will give it a go".
Having been linked with an exit from the Manchester club in January, many now believe the 25-year-old is happy to continue at the Red Devils considering how things have changed under the Norwegian.