Arsenal fell to just a second Premier League defeat of the season as James Tarkowski's header gave Everton the perfect start under new manager Sean Dyche in a 1-0 win at Goodison Park on Saturday.
Tarkowski was fundamental to Dyche overachievements in keeping Burnley in the Premier League for six consecutive seasons between 2016 and 2022 and the centre-back rose highest to power home McNeil's corner on the hour mark.
Chelsea manager Graham Potter pleaded for time to gel his expensive collection of new stars after the Blues were held 0-0 at home by Fulham on Friday.
Fulham had secured a first victory in the west London. Marco Silva's men sit two points and three places above their local rivals in the table in their first season back in the top flight.
Kai Havertz had a hat-trick of big chances to break the deadlock before half-time. The German failed to get enough contact on Thiago Silva's brilliant pass to divert the ball beyond Bernd Leno.
Enzo Fernandez made his Chelsea debut after becoming the most expensive player in British football history with a £107 million move ($132 million) from Benfica.