Both Chelsea and Liverpool maintained their perfect starts to the English top-flight season with wins over Cardiff and Tottenham respectively, while West Ham climbed off the bottom of the table with a 3-1 success away to Everton that gave them a first league victory under manager Manuel Pellegrini.

Here are five things we learned from the Premier League this weekend:

Chelsea’s Hazard hard ball pays off

Liverpool’s upgrades in the transfer market meant they were expected to push City for the title, but Chelsea’s 100% start was not as confidently foreseen after a chaotic summer at Stamford Bridge.

Chelsea caved in to Thibaut Courtois’s demands to join Real Madrid, but crucially didn’t do the same for Eden Hazard. The Belgian has starred rather than sulked at not getting his move, scoring a hat-trick in Saturday’s 4-1 win over Cardiff to take his tally to five goals in just three starts under new manager Maurizio Sarri.

Should Chelsea mount an unexpected title challenge, it will be down to their resilience in holding onto Hazard.

No let-up from Liverpool

The Merseyside club won the last of their then-record 18 English titles in 1990 – before the Premier League was formed – but optimism is growing after a statement 2-1 win over Tottenham Hotspur kept them on maximum points.

Manager Jurgen Klopp called it Liverpool’s best game of the season after a surprisingly easy afternoon at Wembley as Spurs struggled to penetrate until Erik Lamela’s injury-time strike.

Liverpool have so far amassed a perfect 15 points, trailing Chelsea on goal difference – even without any goals so far from Mohamed Salah, who totted up an astonishing 44 in all competitions last season.

Sane and Silva showcase City’s depth

It says much for the wealth of options on offer to Manchester City manager Pep Guardiola that he could afford to leave out last season’s Young Player of the Year Leroy Sane for the first month of the season.

Sane scored inside two minutes of his return to the starting line-up in a 3-0 cruise over Fulham on Saturday that kept City nestled just two points behind the leaders. Guardiola has been reportedly keen to improve Sane’s attitude, but the same can’t be said for Bernardo Silva.

The Portuguese had to wait for his time to shine during City’s record-breaking campaign last season, but is currently Guardiola’s main man in midfield with Kevin De Bruyne sidelined by a long-term knee injury.

“It’s almost impossible to be more pleased with him (Silva) as a manager,” said Guardiola. “That’s why he deserves to play all the minutes he’s playing.”

Mourinho smiles at last

Jose Mourinho was relaxed and contented after Manchester United held on to beat Watford 2-1 on Saturday – a million miles away from his spikiness of recent weeks.

He singled out Marouane Fellaini and Romelu Lukaku for praise and even spoke warmly of the match officials when asked about the late sending-off of Nemanja Matic. “I don’t know,” he said. “The only thing I know is that (referee) Mike Dean was very good and the assistants were very good.”

And he drew a laugh when he joked about goal-scorer Chris Smalling’s new haircut. “He was good,” Mourinho said. “The only thing I don’t like in Chris at this moment is the haircut but I am nobody to tell him that.”

Hammers’ faith rewarded

Such is the febrile atmosphere of the Premier League, there was speculation that new West Ham manager Manuel Pellegrini, despite being given £100 million ($129 million) to spend on players in pre-season, might be sacked after starting the campaign with a run of four straight defeats.

But a 3-1 win away to Everton on Sunday quelled those concerns, at least for the time being, and gave the Chilean an extra reason to celebrate his 65th birthday.

As a former Manchester City manager, Pellegrini is aware of the rollercoaster nature of life in the Premier League, but victory at Goodison Park allowed him to proclaim a long-term vision for the east London club. “We score goals and always try to continue scoring goals. I saw the players working every day of the week... I am convinced and the players are convinced.”