Everton manager Ronald Koeman is under mounting pressure after his team lost 1-0 at home to Burnley on Sunday, while Liverpool drew 1-1 at Newcastle United as the Merseyside clubs continued to struggle in the Premier League.
Liverpool's latest slip allowed Arsenal, which beat Brighton 2-0, to leapfrog it into fifth place as the chasing teams scrambled to keep up with the ferocious pace set by the Manchester clubs who are five points clear at the top.
City and United have 19 points ahead of Tottenham Hotspur on 14, after it won 4-0 at Huddersfield Town on Saturday, with Chelsea, which lost 1-0 at home to Manchester City also on Saturday, and Arsenal both on 13.
Sixth-placed Burnley has 12 points, above Liverpool on goal difference, as its first league win at Goodison Park since 1976 saw it continue its best start to a Premier League season.
Sean Dyche's side has taken eight points from four away games — more than it managed in the whole of last season.
Jeff Hendrick scored the only goal after 21 minutes, finishing off a magnificent team move in a game that brought more speculation about the future of the under-fire Koeman.