Elsewhere, Aleksandar Mitrovic and Glenn Murray were among the goals at the Amex Stadium as Fulham and Brighton played out an entertaining 2-2 draw.

But it was a different story for Christian Benteke, whose Crystal Palace side were beaten by Southampton at Selhurst Park. Benteke is yet to score this season.

BBC Sport looks at the best stats from Saturday's Premier League action.

• Liverpool's 2-1 win at Leicester means they have won their first four league games for the first time since 1990-91.
• The Reds' victory at the King Power Stadium also means they have not lost an away league game after scoring the first goal since December 2016.
• Chelsea also won on Saturday, beating Bournemouth 2-0 at Stamford Bridge to record their fourth win in four for the first time since 2014-15.
• Mitrovic scored Fulham's second in their draw with Brighton, which means he has netted more goals in English league football than any other player since making his Cottagers debut in February (16).
• Only Mohamed Salah (13) and Sergio Aguero (12) have scored more home goals in 2018 than Brighton's Murray (8, level with Harry Kane).
• In Huddersfield's 1-1 draw with Everton, there were just 87 seconds between Philip Billing giving the Terries the lead and Dominic Calvert-Lewin's equaliser for the Toffees.
• Huddersfield have not won any of their past 15 away games against Everton in all competitions (D3 L12), since winning 2-1 at Goodison Park in September 1937.
• Crystal Palace have lost all 10 league games since the start of last season when Wilfried Zaha has not appeared. Roy Hodgson's side were beaten 2-0 by Southampton at Selhurst Park.
• Benteke has scored just three goals in his past 36 Premier League appearances for Palace, after netting 15 in the 35 before that.