Picked out by Dominic Calvert-Lewin on the stroke of half-time, the 31-year-old immediately delivered on his highly romanticised return with the only goal of a cagey encounter.
The well-taken header lifted Rooney's Premier League haul to 199 goals and set Everton's new era into motion as five players made their top-flight debut for the Toffees.
After enduring a tough end to his time with Manchester United, the former England captain is savouring a second chance with his boyhood club.
"To play for this football club again is a huge deal for me," Rooney told Sky Sports.
"To score in my first game in the Premier League back at Goodison, the winning goal, it doesn't get much better.
"Today a good Stoke team made it difficult but it's important you win.
"We've got some tough fixtures coming up and it was important we got off to a good start and that will give us all confidence going into the next game."