United’s win, which took them to within a point of the top five in the Premier League, came courtesy of goals from Andreas Pereira and Marcus Rashford and a Davy Propper own goal.
The victory was all the more impressive given that Solskjaer fielded the youngest starting line-up seen in the Premier League this season — an average age of 23 years and 350 days.
At the end of a week in which they also beat Partizan Belgrade, the mood around United has improved markedly.
“I think it was our best performance of the season. How that didn’t end up five, six, seven, we don’t know, the players don’t know,” said a delighted Solskjaer.
“It was exhilarating, entertaining and great to see that they enjoyed themselves. Since the last international break we have had five wins and we’ve had a lot of answers to what we’re trying to do.
“If they don’t get confidence from this, I don’t know what to tell them.”
– United double –
United struck twice in two first-half minutes, first, in the 17th minute, when a United counter-attack saw Fred find Anthony Martial, who linked with Pereira for a shot that took an unkind deflection off Dale Stephens, wrong-footing goalkeeper Mathew Ryan on its way in.
United supporters were still cheering that impressive start when they were handed double cause for celebration from a deep free-kick that Fred floated into the Brighton area.
Harry Maguire rose powerfully, causing panic for Ryan and his defence, and with Brighton slow to react, Scott McTominay forced the ball over the line, via a final touch by Propper.
It was a scintillating spell of football from a side that, before Thursday’s Europa League win, had not scored two first-half goals at Old Trafford for nearly 10 months — since, coincidentally, a win over Brighton in mid-January.
If Fred had been more fortunate with a 61st-minute strike that Ryan fumbled onto his bar to catch at the second attempt, the afternoon could have been far more comfortable.
As it was, there was a worry for United in the 64th minute when Brighton halved arrears from a Pascal Gross corner, met by Lewis Dunk, who headed in from six yards despite the close attention of Maguire.
United’s response was swift and clinical, however, with the Reds restoring their two-goal cushion just two minutes later.
It came from a blistering counter-attack and a beautifully weighted through ball from Fred, which Martial took in his stride. He brushed off Shane Duffy and rounded Ryan before pulling back for Rashford to convert.
Rashford would follow that, moments later, with an astonishing miss as he failed to find the back of an open net from six yards after fine work and accurate cross from Daniel James.
Teenage full-back Brandon Williams, making his first league start, James and Rashford were all denied by Ryan as United threatened to make the victory even more emphatic, while McTominay suffered a worrying late ankle injury which will be assessed on Monday.
“These are young boys, there are going to be ups and downs,” said Solskjaer.
“But today they started off on the front foot, grew in confidence and then it was just a question of how many are we doing to get? That’s the feeling I got.”
