After James McCarthy had given the Toffees an early lead at Goodison Park, Stones rose highest to meet a 35th-minute Leighton Baines corner and head home via the crossbar.
Ashley Young can't stop John Stones' header finding its way in
Stones, who joined Everton from Barnsley two years ago, was playing his 50th game for the club and said his maiden strike was a “special feeling”.
“It has been a long time, I have had a lot of pressure from players and staff saying I need to get a goal, so it’s a special feeling for me,” said the 20-year-old who has four England senior caps.
“To keep a clean sheet and score three goals against Manchester United is a big day for us and keeps us on a run.”
Kevin Mirallas added a third on 74 minutes to lift Everton into the top half of the Premier League.
Boss Roberto Martinez, who started with seven Englishmen, including senior internationals Baines, Phil Jagielka and Ross Barkley, praised the young centre-back.
He said: "It would be really, really unfair to only highlight one individual after today's performance because we showed incredible focus and mentality.
"But I think John deserves his moment because it's his first goal for Everton - that is an incredible memory.
"I also think his defensive performance was the best I have seen since he has joined the first team.
Gary Cahill gets close to Olivier Giroud at the Emirates
"Phil Jagielka is probably the perfect man to learn from, but, at the young age of 20, to have that composure and style on the ball was magnificent.
"The way he defended against the likes of Wayne Rooney, Marouane Fellaini and Radamel Falcao showed real maturity."
As well as England captain Rooney, the United team also contained Ashley Young, Luke Shaw and Chris Smalling.
In London later in the afternoon, Gary Cahill, who was named in the PFA Team of the Year, started for Chelsea as they moved a step closer to clinching the Premier League title.
The Blues drew 0-0 with rivals Arsenal at the Emirates to edge ten points clear at the top of the table with five games remaining.
Arsenal are now level on points with second-placed Manchester City, but the Gunners have played a game less.
England forwards Danny Welbeck and Theo Walcott came off the bench in the second half for The FA Cup Finalists.
