The striker, 31, opened the scoring in the 35th minute of the friendly in Tanzania to announce the start of his second spell with the club after 13 years at Manchester United.
Roo’s goal had echoes of his first for the Toffees against Arsenal back in 2002 — just five days short of his 17th birthday.
Before scoring, the Scouser had been embraced by a fan wearing a United shirt who had raced onto the pitch.
And Rooney, who rejoined the Toffees earlier this month, could not have asked for a better start to life under Koeman.
After taking a touch with his left foot, he moved the ball on with his right before unleashing a strike to beat keeper Boniface Oluoch all ends up.
The Tanzania National Stadium erupted, while Rooney pointed both hands to the sky and looked to the heavens as his team-mates lapped up what Evertonians hope will be the first of many goals to come.
But the lead lasted just two minutes, with the impressive Medie Kagere finding space in the box from a corner to power a header past Maarten Stekelenburg to ensure the sides went in level at the break.
It was all change in the second half as Koeman sent out a new XI featuring Dominic Calvert-Lewin leading the line.
Rooney was joined on the bench for the rest of the game by Aaron Lennon, who had made his first appearance since February 11 after receiving treatment for a stress-related illness.
New signing Michael Keane saw his header nodded home by Calvert-Lewin — only for the goal to be ruled out for offside.
With Roo watching on, Kieran Dowell hit the crossbar from a short free-kick before smashing home the winner nine minutes from time.