London - Manchester City were in sparkling form during a 5-0 win over Burnley while Liverpool kept pace with the leaders by grinding out a 1-0 victory at Huddersfield.
Amid a touchline flare-up, there were encouraging signs for Manchester United manager in a 2-2 draw away to former club Chelsea, with Tottenham remaining in title contention after a 1-0 win at West Ham.
Elsewhere, Everton continued to climb up the table with a 2-0 victory at home to Crystal Palace - their third straight league win.
Here are five things learned from the Premier League this weekend:
Premier League champions Manchester City are moving ominously into gear, boasting nearly 2.9 goals per game in the Premier League after nine matches -- an even higher strike rate than over the course of their record-breaking return last season.
"The goals were so outstanding, beautiful, beautiful goals," said City manager Pep Guardiola.
Mohamed Salah has made a slow start to the new campaign after scoring 44 goals in a memorable debut season for Liverpool.
The Egypt international came into Saturday's match against Huddersfield with just one goal for Liverpool in his past eight matches but a trademark clinical finish gave him his fourth Premier League goal of the season.
His strike was his 50th goal for English clubs - Liverpool and Chelsea - in just 83 games in all competitions.
United offer Mourinho hope
Just as in a dramatic 3-2 victory over Newcastle before the international break that kept Jose Mourinho in a job, it took Manchester United going behind for the Red Devils to summon a response against Chelsea. But although Ross Barkley's 96th-minute equaliser denied United victory at Stamford Bridge, there were plenty of positives for the United manager.
The Portuguese's adventurous line-up featuring Paul Pogba, Juan Mata, Marcus Rashford, Anthony Martial and Romelu Lukaku was rewarded with Martial's double.
Defensive deficiencies remain a concern, but United have shown in their past two games what they are capable of when given the freedom to go forward and Mourinho could now remain in charge at Old Trafford for a while yet.
No signings, no problem for Pochettino?
Assailed by criticism after failing to sign a single player during the close-season transfer window, Tottenham Hotspur have mounted the perfect response.
A mature 1-0 win at West Ham made it the best start to a season for Tottenham in the Premier League era.
Erik Lamela's first-half header and a composed defensive display sealed a fourth successive league victory for Mauricio Pochettino's team.
Asked if his side's progress proved they were right not to splash out like their title rivals, the manager refused to claim it was part of a plan.
"If you said to me you are so clever because we didn't sign players, I would not tell you I am a genius because after nine games we made the best start for the club in the Premier League.
"To be honest, the truth is we try to sign players."
Silva service succeeding at Everton
Managers often get plenty of blame when results go against them, so it's only fair to give them some credit for their team's victories.
Everton boss Marco Silva might have been tempted to shore up his defence late on against Crystal Palace but instead he sent on a trio of attacking substitutes and saw two of them, Dominic Calvert-Lewin and Cenk Tosun, score in a 2-0 win at Goodison Park.
"We (the staff) are here to make decisions, it is not just the starting XI," said Silva.
"We have solutions on the bench."