Leicester 2-3 Liverpool
Philippe Coutinho has scored more goals from outside the box (16) than any other player in the Premier League since his debut
Jamie Vardy missed a penalty as Liverpool held on to beat Leicester at the King Power Stadium.
Simon Mignolet saved Vardy's spot-kick in the 73rd minute to preserve the Reds' lead, which had been given to them by goals from Mohamed Salah, Philippe Coutinho and Jordan Henderson.
Shinji Okazaki and Vardy pegged Liverpool back at 2-1 and 3-2, but Jurgen Klopp's men did just about enough to collect a first win in five games in all competitions.
Goals: Okazaki 45+3', Vardy 69' -- Salah 15', Coutinho 23', Henderson 68'
Burnley 0-0 Huddersfield
The first half at Turf Moor did not feature a single shot on target
Burnley and Huddersfield couldn't be separated at Turf Moor, which played host to a dull goalless draw.
After a first half severely lacking in attacking quality, both sides showed more ambition after the break. Neither was able to land a decisive blow, however, with Sean Dyche and David Wagner ultimately forced to settle for a share of the spoils.
Everton 2-1 Bournemouth
Niasse scored his first Premier League goals for Everton almost 20 months after joining the club
Oumar Niasse was the unlikely hero as Everton came from behind to beat Bournemouth at Goodison Park.
Josh King gave the Cherries the lead just three minutes into the second half, but forgotten man Niasse - who replaced Wayne Rooney after the 31-year-old sustained a nasty facial injury - scored two quick-fire goals in the final 15 minutes to turn the game on its head.
This was a much-needed win for Ronald Koeman's side after three league games without a goal, while Bournemouth remain in the relegation zone.
Goals: Niasse 77', 82' -- King 48'
Man City 5-0 Crystal Palace
Crystal Palace are the first side in English Football League history to lose their first six games of the season without scoring
A brace from Raheem Sterling and goals from Leroy Sane, Sergio Aguero and Fabian Delph moved Manchester City clear of second-placed Manchester United on goal difference.
Palace had their chances in the first half, Ruben Loftus-Cheek hitting the post and then dragging another shot wide from a promising position, but it was City who scored the all-important opener through Sane in the 44th minute.
The German turned provider after the break, teeing up Sterling for City's second, before the England international notched his fourth of the season on the hour. Aguero and Delph added to Palace's misery by getting in on the act late on, as the Eagles failed to score for a sixth consecutive game.
Goals: Sane 44', Sterling 51', 59', Aguero 79', Delph 89'
Southampton 0-1 Man United
No player has scored more goals in their first six Premier League games for Man United than Romelu Lukaku (6, level with Louis Saha)
Romelu Lukaku was the match-winner as Manchester United eked out a narrow victory at St Mary's.
The Belgian striker opened the scoring in the 20th minute, converting at the second attempt after Fraser Forster saved his initial effort from Ashley Young's cross. United controlled proceedings for the remainder of the first half, but Southampton improved after the break and went close to an equaliser through Oriol Romeu and Shane Long.
Jose Mourinho's men weathered the storm, though, and remain level on points with table-toppers Manchester City.
Goals: Lukaku 20'
Stoke 0-4 Chelsea
No player has more goals/assists in his first six Premier League games for Chelsea than Alvaro Morata (8)
Chelsea returned to winning ways after their goalless draw with Arsenal last weekend, as Alvaro Morata's hat-trick made the difference at the Bet365 Stadium.
Morata broke the deadlock after just 82 seconds, the former Real Madrid man racing onto Cesar Azpilicueta's long pass and slotting the ball past Jack Butland. Compatriot Pedro then made it two after half an hour, capitalising on a mistake from Darren Fletcher to double the champions' lead.
Morata made sure of the victory with a fine finish in the 77th minute, before completing his hat-trick with a tap-in after some excellent work from Azpilicueta and Cesc Fabregas.
Goals: Morata 2', 77', 82' Pedro 30'
Swansea 1-2 Watford
Watford have now won three successive top-flight away games for the first time in the club's history
Richarlison's last-minute goal brought Watford victory at the Liberty Stadium.
The visitors were much the better team in the opening period and deservedly took the lead in the 13th minute, Andre Gray prodding the ball home from six yards out. Swansea improved significantly after the interval, though, and were back on level terms when substitute Tammy Abraham converted from close range after Wilfried Bony's effort was pushed into his path by Heurelho Gomes.
Swansea pushed hard for a winner but could not find it, as Watford and Richarlison stunned the hosts late on.
Goals: Abraham 56' -- Gray 13', Richarlison 90'
West Ham 2-3 Tottenham
Harry Kane now has the best minutes-per-goal ratio (113) in Premier League London derbies (minimum 10 goals)
Harry Kane scored twice to earn Tottenham all three points in an entertaining London derby.
The England international netted two goals within four first-half minutes to put Spurs in a commanding position, before Christian Eriksen made it three on the hour-mark. West Ham pulled one back through Javier Hernandez soon after, though, and were further boosted when Serge Aurier was sent off with 20 minutes left to play.
Slaven Bilic's side eventually grabbed a second, Cheikhou Kouyate powering home a header from Arthur Masuaku's cross, but it was a case of too little, too late as Tottenham held on.
Goals: Hernandez 65', Kouyate 87' -- Kane 34', 38', Eriksen 60'
