The 18-year-old has now got 13 goals in his first season in senior football while also becoming the first United player to score six Premier League goals before turning 19.
"He's a special talent, a special kid that we are going to look after and try to develop into a top top player," said Solskjaer.
"He's doing well now but he is still young and has things to learn. He knows that but we have a special talent there we have to nurture."
Greenwood's goal came after a driving run into Brighton's penalty area and after Fernandes doubled the lead before half-time. The Portuguese midfielder scored the third from Greenwood's cross following a swift counter-attack.
"He's getting better," said Solskjaer. "You can see clearly that he's maturing and improving, he's only 18 still so we will see more from him.
"I've said it throughout the year that as long as we can get him faced up in and around the box he'll create chances for us but in this game his hold-up play and his link-up play and general movement was fantastic as well."
After the match Fernandes said he believes United can squeeze into the league's top four, with fourth-placed Chelsea two points ahead of them with a game in hand, and was quick to credit his teammates for flourishing under Solskjaer.
"We are fighting for a place in the Champions League and we know we can achieve this," Fernandes said.
"I don't want to talk too much about me and Paul Pogba, we are happy to play together but I am happy to play with everyone. We can combine together, we have qualities, but we know that we have teammates who can do well.
"We knew that we needed to push forward and to try and score from minute one. I was lucky with the first goal and the second goal was amazing, an amazing pass from Mason."