Stanislas, who netted a late equaliser in this corresponding fixture last season, struck midway through a first-half which also saw the hosts hit the woodwork twice through Jack Wilshere and Harry Arter.
Bournemouth, meantime, coming into this game off the back of a chastening 4-0 defeat at Manchester City last weekend, and although Eddie Howe's men can perhaps be forgiven such a heavy defeat at the Etihad Stadium, they have started the season poorly.
"But we know we will not win every game".
Things have been going well at both ends of the pitch in the league, with Everton conceding only three goals and scoring 10.
Everton, lacking rhythm and fluency, were unable to add to their four wins and one draw in the league, perhaps still smarting from their 2-0 midweek EFL Cup home defeat to Norwich. I was comfortable with that they showed but, of course, it was not good enough because we did not score a goal. They had a very good season past year and it's a hard one. It's a pity because we need to start like this. "But we have a strong team".
"I don't think [Lukaku's potential absence] changes anything but he's still a contracted player of Everton".
"It is all up to the player whether he doesn't leave, I can't understand it, but that is normal". "From the beginning he was comfortable".
The Senegalese midfielder made the move to Goodison Park from relegated Aston Villa in the summer and he has been oustanding for Koeman's side so far as the Blues have made an unbeaten start in the Premier League. "He's a great signing". "He can improve. He will be stronger and more clever and that's all about experience".