Romelu Lukaku was on target again as Manchester United continued their fine early-season form with a second successive 4-0 win on Saturday, this time at Swansea City. Eric Bailly, Paul Pogba and substitute Anthony Martial also found the net at the Liberty Stadium, giving Jose Mourinho's side their second big win after last weekend's 4-0 victory over West Ham United. Sadio Mane struck in the 73rd minute to give Liverpool a 1-0 home win over Crystal Palace and get Jurgen Klopp's side up and running after their 3-3 draw at Watford on the opening weekend.
"The team was confident from the first minute," said Mourinho after a result that means United have scored four goals in their first two league games for the first time in 110 years.
"I like to see the confidence that the players are having in this moment. There's no panic. The team was always confident and always trying to move the ball. I'm really happy."
Having had to work hard to break Swansea down, United went in front just before half-time when Bailly stabbed in his first goal for the club after Lukasz Fabianski had pushed Pogba's header against the bar.
Attacking changes left Swansea vulnerable at the back in the latter stages and United took full advantage to score three goals in the space of just four minutes.
In the 80th minute Henrikh Mkhitaryan teed up Lukaku for his fourth goal in three United games since signing from Everton.
Mkhitaryan then freed Pogba to beat Fabianski with a delightful dinked finish before Martial tucked in a fourth.
At Anfield, Liverpool manager Klopp made five changes to the team that won 2-1 at Hoffenheim in their Champions League play-off round first leg in mid-week.
Beaten 3-0 at home by Huddersfield Town on the opening weekend, Palace produced a much more solid display, but were undone with 17 minutes to play when Mane seized upon a loose ball to fire home.
- Austin late show -
"It was a hard job. I have no idea how much we had the ball, but it was a lot," Klopp told Sky Sports.
"We were really awake and defended really well and I loved the goal because it was not a clear situation. We had other chances, but I am completely happy with how we did the job today."
Arsenal visit Stoke City in the late game.
Narrowly beaten 4-3 by Arsenal in the season's opening match, 2016 champions Leicester City hit back to beat Brighton and Hove Albion 2-0 at the King Power Stadium.
Shinji Okazaki broke the deadlock after just 52 seconds, tapping in after Mathew Ryan saved from Riyad Mahrez, and Mahrez's corner set up Harry Maguire to head in Leicester's second early in the second half.
Charlie Austin scored a 93rd-minute penalty to earn Southampton a last-gasp 3-2 home win over West Ham.
Goals from Manolo Gabbidini and Dusan Tadic, the latter a penalty, put Saints 2-0 up and West Ham new boy Marko Arnautovic was sent off in between for an elbow on Jack Stephens.
Javier Hernandez's first two West Ham goals drew the 10 men level, only for Austin to secure victory from the spot after Maya Yoshida was fouled by Pablo Zabaleta.
Hal Robson-Kanu was hero and villain as West Bromwich Albion won 1-0 at Burnley.
The Wales striker came off the bench to score a 71st-minute winner, but was then sent off for leading with his arm in a challenge on Matthew Lowton.
Brazilian youngster Richarlison scored his first goal in English football and Etienne Capoue opened his account for the season as Watford claimed a deserved 2-0 win at Bournemouth.
- Jese Rodriguez Sinks Arsenal -
Jese Rodriguez made a memorable start to life at Stoke City by scoring the only goal of a 1-0 victory over Arsenal at the bet365 Stadium on Saturday. The Spanish forward, a loan signing from Paris Saint-Germain, finished crisply in the 47th minute to bring Arsene Wenger's side down to earth after their opening 4-3 win over Leicester City.
It was an early blow to Arsenal's title aspirations and left them three points behind early pace-setters Manchester United, who won 4-0 for the second game running at Swansea City.
Jese, 24, only joined Stoke on Wednesday and he was quick to make an impression on the fans of his new team.
After driving at Arsenal's back four from halfway, he swapped passes with Saido Berahino and then drilled a left-foot shot past the advancing Petr Cech.
Arsenal, who remain without the injured Alexis Sanchez, thought they had equalised in the 72nd minute when Alexandre Lacazette lashed home, but it was chalked off due to a marginal -- but correct -- offside.
Stoke had not beaten Arsenal since December 2014.