Midfielder Andreas Pereira and striker Marcus Rashford scored either side of a Davy Propper own goal on Sunday to hand United their biggest home league win since the opening weekend of the campaign in August.
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There was a sense of optimism at Old Trafford as United continued to attack late in the second half to extend their lead, with Fred, Anthony Martial and Rashford testing Brighton goalkeeper Mat Ryan.
"I think it's our best performance of the season," Solskjaer told reporters.
"How we didn't end up with five, six, or seven we don't know, but exhilarating and entertaining and great to see the boys enjoy themselves."
United's front three of Rashford, Martial and Daniel James showed electric pace on counter-attacks but Solskjaer reserved special praise for 19-year-old left back Brandon Williams, who was impressive in his first league start.
Man United's attacking trio gives Solskjaer reason for optimism
Solskjaer selected Williams ahead of experienced Argentine international Marcos Rojo in the starting lineup, and said that it will be difficult not to pick him again.
"Brandon was excellent. He's played well before, but first start at Old Trafford in a Premier League game, you don't know how he's going to react," Solskjaer added.
"He's done nothing wrong since he's come in and making it hard for me (to leave him out), definitely."
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