Coupled with progress in the League Cup, Everton has made its best start to a season since the 19th century with seven wins out of seven.
Everton made a strong start, with Coleman and Calvert-Lewin forcing early saves from Matt Ryan but then made the breakthrough with a quarter of an hour on the clock.
Dominic Calvert-Lewin continued his impressive goal scoring run as he opened scoring for Everton on 16 minutes.
Fortunately for Ancelotti he has no such worries at the other end of the pitch where Calvert-Lewin, after passing up a relatively straightforward chance a man in his form should have taken after 82 seconds, continues to excel.
It is now four wins out of four in the Premier League for Everton which place them top on the log in 12 points.
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But on a wet day the ball slipped from his grasp, presenting Maupay with a simple tap-in.
With three goals and three assists in five games for Everton in all competitions this season, James has doubled his return from his 14 appearances with Real Madrid last season (one goal, two assists).
The Nigerian was then involved again as Everton grabbed their fourth 20 minutes from time with Iwobi playing a flawless through ball for Abdoulaye Doucoure who in turn found Rodriquez who tapped home for his second of the game to make it 4-1.
The Toffees have also won their opening four games in a top-flight season for the first time since 1969-70, when they went on to win the title.
"Now there is the worldwide break we can have a rest".
A pause may also benefit the Seagulls, for whom Yves Bissouma volleyed home an added-time consolation, after a third defeat in a week and a ninth in succession on the road in the Premier League.