In what was a fairly quiet first period, it was the home side who threatened first, when Leighton Baines found Sandro Ramirez but the new signing's shot on the turn flew wide of the far post.
The home side took the lead on the stroke of half-time, when Dominic Calvert-Lewin curled in a cross and Wayne Rooney was there to head past Jack Butland in his first Premier League game for the Toffees since re-joining the club in the summer.
Mark Hughes's side rarely threatened in the first half but after the interval they came close to equalising when Darren Fletcher tried his luck from outside the area but his shot was just wide.
Ronald Koeman's side almost doubled their lead when Calvert-Lewin cut inside and curled in a shot but Butland was equal to it and tipped it around the post.
Both sides pushed for goals after that but the home side held on to make it a triumphant homecoming for Rooney, who scored his 199th goal in the Premier League with the winner.