Rooney, who was full of invention and energy throughout, rose well to meet a fine Dominic Calvert-Lewin cross with a looping header into the far corner on the stroke of half-time.
The former England captain rejoined his boyhood club last month after 13 years with Manchester United and he instantly looked at home.
“To play for this football club again is a huge deal for me and to score at Goodison in my first game back, it doesn’t get much better. A great moment,” said Rooney.
“It was a tough game and we were a bit fortunate to go in 1-0 up at halftime. I thought we were the better team in the second half and deserved to win,” he added.
The 31-year-old, playing just behind debutant Spanish striker Sandro Ramirez, delivered some clever passes and fed the lively...