Arsenal came from behind to beat Swansea City 2-1 while Crystal Palace managed a draw against West Ham.
Manchester City continued their superb start to the season with a 3-2 win at West Bromwich Albion on Saturday to keep five points clear at the top of the Premier League.
Leroy Sane put City ahead after 10 minutes with a left-foot shot into the corner of the net for his eighth goal of the campaign.
West Brom equalised quickly when Jay Rodriguez got in behind the defence but City retook the lead through Fernandinho after the Brazilian's long shot took two deflections before hitting the post and rolling into the net.
City substitute Raheem Sterling added the third, tapping in from close range after a cross from Kyle Walker at the end of a patient move before Matt Phillips snatched a late consolation for West Brom following a mistake by Nicolas Otamendi.
Earlier, Manchester United kept within five points of their neighbours with a crucial 1-0 win over fellow contenders Tottenham Hotspur.
Liverpool back on track
Liverpool put their recent Premier League frustrations behind them to breeze past Huddersfield Town 3-0 on Saturday with Daniel Sturridge's goal setting up the victory.
Mohamed Salah missed a first-half penalty but that was largely forgotten by the end as Juergen Klopp's side produced a vibrant second-half display with Roberto Firmino and Georginio Wijnaldum on target after Sturridge broke the deadlock.
Their first win in four league games kept Liverpool in touch with the top four, moving them up to sixth spot with 16 points from 10 games, three behind fourth-placed Arsenal.
Arsenal beat Swansea 2-1
Arsenal came from behind to beat Swansea City 2-1 in the Premier League on Saturday, with second-half goals from Sead Kolasinac and Aaron Ramsey helping them overcome the injury-weakened visitors.
Victory for the Gunners in Arsene Wenger's 800th Premier League match in charge means champions Chelsea, who play in the day's late kick-off at Bournemouth, must win to retake fourth place in the table.
Swansea, playing without injured striker Wilfried Bony, midfielder Renato Sanches and defender Martin Olsson, took the lead in the 22nd minute against the run of play, when Sam Clucas raced into the area and slotted the ball neatly beneath Arsenal goalkeeper Petr Cech.
Bosnian left back Kolasinac equalised in the 51st minute, before Ramsey put the home side ahead in the 58th with his third goal of the season.
Palace salvage draw against West Ham
Winger Wilfried Zaha scored in the seventh minute of added time to salvage a 2-2 draw for Crystal Palace against West Ham United at Selhurst Park on Saturday.
England goalkeeper Joe Hart was beaten by Zaha's low shot into the bottom corner after making several fine saves that had seemed enough to give Hammers victory.
Striker Javier Hernandez fired the visitors ahead after half an hour from Aaron Cresswell's cross and Andre Ayew put them two up before half-time with a shot from outside the box into the top corner.
West Ham, who had lost their previous league match 3-0 at home to Brighton & Hove Albion, were put under intense pressure in the second half and Palace pulled a goal back with Luka Milivojevic's penalty in the 50th minute, before Hart saved Yohan Cabaye's free kick and an earlier effort by Zaha.
Palace, whose only win in the league came against Chelsea two weeks ago, remain firmly rooted to the bottom of the table with four points from 10 matches, while West Ham are in 16th place on nine.
Stoke beat Watford for first away win
Stoke upset the form book to earn a first Premier League away win of the season as they battled to a 1-0 victory over high-flying Watford at Vicarage Road on Saturday.
Midfielder Darren Fletcher scored his first goal for Stoke with a superb volley from a Xherdan Shaqiri corner to put the visitors into a 16th-minute lead.
Watford created plenty of chances in the second half, but failed to find an equaliser with Brazilian Richarlison guilty of missing promising openings.
Watford suffered their second successive defeat and slipped to seventh while Stoke climbed up to 13th.
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