Lukaku missed two good early chances that were saved by Angus Gunn before he struck twice with two clinical right-foot finishes.
But the away side grew into the game and started to put pressure on the Manchester United defence with some incisive football.
There were a number of standout performers in the Southampton side at Old Trafford, with Valery very much one of them, and fans of the Hampshire outfit were quick to acknowledge him after the final whistle.
But the forced introduction of Dalot proved significant with the young Portuguese defender, forced into midfield, sending over a right-wing cross with his very first touch which Rashford headed just wide.
Sumptuous strikes from Yan Valery and James Ward-Prowse gave Manchester United a real scare but ultimately the home team prevailed in a game tinged by controversy.
"All these top players that we have, they need players to challenge them, because no one should feel 100 per cent secure to be in the starting XI in the next game".
And the home side got an opportunity to add gloss to the scoreline.
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But that was not the end of the scoring as Lukaku snatched a late victor - and there was even time for Paul Pogba to see a stoppage time penalty saved.
United now sit fifth in the Premier League, one place and one point behind fourth-place Arsenal. Now Ole Gunnar Solskjaer's bandwagon is gaining such momentum that his players head to the French capital quietly believing they could yet reach the last eight.
The calls to make Solskjaer the permanent boss are growing as his unbeaten league run continues, and BT Sport pundit Rio Ferdinand believes that his former teammate has earned the right to lead United into next season, as detailed in the Mail On Sunday. It was an open game and they came here to beat us. PSG are in a dominant position as they lead the tie 2-0. My team did fantastic and the boys did great in the second half.
"The belief is there, they have gone so long without losing games (domestically) and are raring to go".
"Rom is a goalscorer, he keeps practising every single day and has quality". I wasn't standing there jumping and saying: "This is the best signing we've got, brilliant, I'm delighted with this".
The last-gasp win was a timely shot in the arm - both in terms of propelling United back into the top four and boosting morale ahead of Wednesday's uphill battle against Paris St Germain in the Champions League.
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