Top three stay unbeaten after Blues and City win
The result means that three clubs - Chelsea, Manchester City and Liverpool - remain unbeaten after 11 matches.
An Alvaro Morata brace and a goal from Pedro handed maximum points to the Blues, who are 12-1 with Hills to win the title in Maurizio Sarri's first season in the dugout.
There were few surprises at the Etihad, where champions City hit a sorry Southampton for six, prompting bookmakers to shave the south coast club's relegation price to as short as 7-2.
The Saints are winless in seven in the league and Mark Hughes has been cut to 21-10 to be the next Premier League manager to leave his post.
City and Chelsea are short prices for their midweek European clashes, with Pep Guardiola's men a general 1-8 to beat Shakhtar Donetsk and the London side 2- 5 to win at Bate Borisov.