Grealish, on-loan from Manchester City, started for Everton and helped them win their first game at the club's new stadium.
Speaking afterwards, Grealish said: "It was massive, our first game at the new stadium and we wanted to put on a show for the supporters. I think we certainly did that.
"I always say playing against Brighton is one of the toughest games with the way they play, so we're very happy to get the win.
"It was great. I absolutely loved my time at Man City – I had a great four years there and won a lot of things, but this summer I felt like it was time for a change and, as I've said before, as soon as I spoke to the manager, David Moyes, on FaceTime, I knew this was the place I wanted to come.
"There were a lot of reasons why I wanted to come here – and today shows why."
On Grealish's display, David Moyes said: "He was game for it; he didn’t try to shirk anything. He didn’t want off after 60 minutes – no chance. He wants to show he’s the real deal.
"He probably has something to prove. I had something to prove over the years at different times. I think sometimes it gives you that challenge you have to be ready to take. Hopefully Jack is."