The 18-year-old Wilson, making his full debut, knocked the ball past keeper Saul Deeney from close range after Chris Iwelumo headed on a long throw by Adam Virgo.
Brighton had been frustrated until then in the spring sunshine by County, who conceded four goals in each of their previous away matches.
The home team dominated the match without forcing Deeney into serious action on many occasions.
Brighton thought they should have been awarded a penalty in the second half when Gary Hart, on in place of Charlie Oatway, was sandwiched inside the area by two Notts defenders.
Referee Andy Hall instead booked the substitute for diving.
David Pipe, County's Welsh international, was stretchered off to hospital for X-rays on an ankle injury following a second half tackle by Oatway which earned the Brighton midfielder a caution.
Brighton manager Mark McGhee said: "It was a professional performance and we deserved the win. We did not know what to expect from County, but they were resolute and made life difficult for us.
"We are up to fourth now and I want us to stay there with a win at Wrexham next Saturday so that we are at home in the second leg of the play-offs."County manager Gary Mills said: "It is a cruel game. Kelvin did very well but there is a positive because he will learn from this.
"He will be playing next Saturday, make no mistake about that. I thought it was an excellent debut.
"We have lost another game but we defended a lot better and kept our shape a lot better."