Manchester United and England's record goalscorer marked his first appearance back in a Blue shirt with a fine effort against Gor Mahia earlier this month and was on target again at the Luminus Arena.
He produced a neat first-time finish at the back post just before half-time after a cross from Sandro Ramirez and later took the captain's armband when Leighton Baines left the pitch.
New £30 million (A$49.25 million) goalkeeper Jordan Pickford made his first appearance for Everton, as did Sandro, and kept a clean sheet before being replaced by Maarten Stekelenburg, who conceded the equaliser.
Former Sydney FC keeper Danny Vukovic wasn't in action for Jupiler Pro League side Genk.