Jurgen Klopp's reign as Liverpool manager began with a hard-fought 0-0 draw at Tottenham, while Chelsea eased the pressure on Jose Mourinho with a 2-0 win against Aston Villa on Saturday.
Klopp's first taste of the Premier League stole most of the attention as the English top-flight returned to action after the international break, but there were plenty of other intriguing sub-plots.
Under-fire Chelsea boss Mourinho saw the troubled champions secure only their third league victory this season, while Raheem Sterling's first-half hat-trick kept Manchester City top of the table with a 5-1 rout of Bournemouth.
Alexis Sanchez ensured second placed Arsenal remain hot on City's heels as his seventh goal in four games kick-started a 3-0 stroll at Watford.
Wayne Rooney ended his 11-month away-day goal drought as Manchester United eased to a 3-0 victory on an emotional day at Goodison Park following the death of former Everton manager Howard Kendall.
Greeted by Germany flags in the away end bearing legends like 'Liverpool Uber Alles', Klopp handed a league debut to 20-year-old striker Divock Origi, who hit the bar in the early stages at White Hart Lane.
But he was also indebted to goalkeeper Simon Mignolet for producing three important saves, which meant that although Liverpool have now won only once inside 90 minutes in their last 10 games, their manager was spared defeat on his first outing.
"This is not the worst sign. I hadn't got the biggest expectations for the game as we only had three days together and Tottenham are a strong and tuned team. It could have been difficult so I'm really satisfied," Klopp said.
Chelsea had made their worst start to a top-flight season since 1978-79, prompting the club to issue a vote of confidence in Mourinho amid reports of a dressing room mutiny.
But they were on course for a first win in four matches in all competitions after a shambolic mix-up between Villa goalkeeper Brad Guzan and Joleon Lescott in the 34th minute allowed Diego Costa to mark his return from a three-game ban with his third goal of the season.
Costa played a signficant role in Chelsea's second goal as well, this time the Spain striker's attempted shot took a big deflection off Alan Hutton for an unfortunate own goal by the Villa defender.
"At the moment, some of my players have lost confidence," Mourinho said.
"But they showed their desire, that they are together and that there were ready to fight for a crucial result."
- Barren run -
At Eastlands, City took just seven minutes to go in front when Sterling prodded past goalkeeper Adam Federici.
City struck again four minutes later when Ivory Coast striker Wilfried Bony tapped in after Federici made a hash of claiming a cross.
Bournemouth's Glenn Murray scored in the 22nd minute, only for England winger Sterling to add City's third in the 29th minute.
Sterling completed his treble in first half stoppage-time and Bony struck again in the 89th minute.
Emotions were running high at Goodison following the death of Kendall aged 69 and there was a minute's silence prior to kick-off, while Everton's players wore black armbands as a mark of respect.
But third placed United, who remain two points behind City, took the lead through Morgan Schneiderlin's first goal since his pre-season move from Southampton in the 18th minute.
Spanish midfielder Ander Herrera doubled United's advantage with a 22nd minute header.
United captain Rooney hadn't scored an away league goal since November last year, but the former Everton forward ended that 17-match barren run with a clinical near-post finish in the 62nd minute.
"I said to my players I'm very proud of them because it is one of our best matches. We needed that because Everton are a very good team," United manager Louis van Gaal said.
Arsene Wenger's Arsenal, two points adrift of City, went ahead when Chile forward Sanchez slotted home in the 62nd minute to maintain his red-hot form.
Substitute Olivier Giroud added the second six minutes later and Aaron Ramsey claimed the third from close-range in the 74th minute.
"Alexis Sanchez is relentless going forward. He is very important for us," Wenger said.
"It was an important win for us. The confidence is there."
Sam Allardyce's first match as Sunderland manager ended in a 1-0 defeat at West Bromwich Albion
Allardyce was unable to secure Sunderland's first league win of the season as Saido Berahino netted in the 54th minute.
West Ham climbed to fourth place after a 3-1 success at 10-man Crystal Palace.
Leicester staged another great escape as they came from two goals down to draw 2-2 at Southampton.
Source: AFP
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