Everton manager Marco Silva has admitted that he is aiming to keep supporters entertained as well as winning games this season
A well-worked free kick saw Theo Walcott open the scoring for the hosts against his former club, before Richarlison made it three goals in two games with a near-post header shortly after the half-hour mark.
Silva was disappointed that his side allowed Southampton to pull one back through full debutant Danny Ings, but the ex-Watford boss believes that Everton were good value for the points.
"It's an important three points for us, it's important that it was enjoyable for our fans as well," he told Sky Sports News. "In the first half we did very well, we tried to do things differently in the second half and manage the game.
"But things were a bit slow, and conceding the goal gave Southampton some belief. After 25-30 minutes of the second half, though, we had enough to score the third goal and we would have deserved it.
"You can manage games in different ways. The only thing I'm not happy with really is conceding the goal from a set piece, we needed to be stronger at that moment, but they didn't have a big chance to score with our organisation."
Everton are unbeaten in their past 14 home league games against Southampton since a 2-0 defeat in November 1997.