Manchester United maintained their 100 percent start to the new season with a 4-0 win at Swansea to remain top of the Premier League.
Eric Bailly opened the scoring and his United account on the stroke of half-time, nudging the ball over the line after Lukasz Fabianski had diverted it onto the underside of the crossbar from Paul Pogba's powerful header.
United then burst into life as the game entered the 80th minute, doubling their advantage when Henrikh Mkhitaryan played in Romelu Lukaku, who made it three goals in two Premier League appearances following his summer move from Everton.
Mkhitaryan produced another fine assist moments later, racing down the right before slipping in Pogba, who flicked the ball over Fabianski, before substitute Anthony Martial then rounded off the scoring in the 84th minute with an excellent solo effort, doubling his tally for the season.
Jese Rodriguez scored on his debut as Stoke beat Arsenal 1-0 at the bet365 Stadium to claim their first Premier League points of the season.
Stoke took the lead two minutes into the second half, with Paris Saint-Germain loanee Jese netting on his debut, slotting past Petr Cech after being played in by Saido Berahino.
Arsenal piled on the pressure as they went in search of an equaliser, with Hector Bellerin, Danny Welbeck, Aaron Ramsey and Mesut Ozil all going close.
They thought they had found it in the 73rd minute when Alexandre Lacazette fired into the top corner of the net following substitute Olivier Giroud's flick, but the goal was disallowed for offside, with Stoke holding on for victory.
Sadio Mane was on target for Liverpool with his second-half winner securing a 1-0 victory against Crystal Palace at Anfield and his side's first league victory of the season.
After a tight first half, Liverpool almost went ahead nine minutes into the second when Daniel Sturridge volleyed at goal from 25 yards out, only for Wayne Hennessey to deny him with the save.
The home side had another chance to open the scoring just a few minutes later as Roberto Firmino curled one from the edge of the box, but his strike went inches wide.
Jurgen Klopp brought on Mohamed Salah and Dominic Solanke as time wore on, and Liverpool eventually found a breakthrough in the 72nd minute with Mane stabbing the ball past Hennessey after Palace's defence had failed to clear the danger.
Charlie Austin netted a last-minute penalty to secure Southampton a dramatic 3-2 win against 10-man West Ham at St Mary's.
Southampton went ahead in the 11th minute through Manolo Gabbiadini, who fired past Joe Hart after being played in by Nathan Redmond to net the club's first league goal at home since April 5.
West Ham were then dealt a further blow in the 33rd minute when Marko Arnautovic picked up a straight red card after catching Jack Stephens with his elbow, and things got even worse five minutes later when Jose Fonte conceded a penalty and Dusan Tadic stepped up to convert from the spot.
West Ham pulled one back on the stroke of half-time when Javier Hernandez slotted home after Fraser Forster had saved Michail Antonio's effort, and the Mexico international was on the scene once again in the 73rd minute to convert after Diafra Sakho had headed against the bar.
But Southampton had the final say after winning a penalty deep into stoppage time, with Austin firing home to secure the three points for the Saints.
Leicester recorded their first win of the season with a 2-0 victory over Brighton at the King Power Stadium.
Shinji Okazaki opened the scoring for Brighton inside the first minute, converting the rebound after Riyad Mahrez's shot had been parried into his path by Maty Ryan.
Brighton had the ball in the back of the net through Glenn Murray, but the goal was disallowed due to offside, and Leicester then doubled their lead 10 minutes after the restart through Harry Maguire, who arrived at the far post to head home Mahrez's corner.
Watford saw off Bournemouth 2-0 at the Vitality Stadium with Richarlison and Etienne Capoue getting the goals.
Watford had a chance to open the scoring just before half-time when Richarlison cut the ball back to Andre Gray, but the striker sent his effort over the bar.
They made no mistake in the 72nd minute, however, with Richarlison touching the ball over the line after Gray had done well down the right, before Capoue doubled their lead with a strike from 25 yards out four minutes from the end.
West Brom made it two wins out of two with a 1-0 victory over Burnley at Turf Moor, though match-winner Hal Robson-Kanu also received a red card.
West Brom thought they had found the breakthrough shortly after the restart when Jake Livermore had the ball in the back of the net but the flag went up for offside on Jay Rodriguez.
They did manage to move ahead 20 minutes from time, with Robson-Kanu shrugging off a defender and striking a low hit past Tom Heaton.
West Brom were reduced to 10 men seven minutes from time when Robson-Kanu was sent off for an apparent elbow on Matthew Lowton, but the visitors manged to hold on for the victory.