Guardiola, Mourinho, Conte, Pochettino & Klopp on Saturday's Premier League action

Manchester City manager Pep Guardiola said his side are "feeling better" about their title challenge this season on a day when the Premier League's top three all won.

City, who defeated Crystal Palace 5-0, lead Manchester United - 1-0 winners at Southampton - on goal difference, with Old Trafford boss Jose Mourinho claiming that the race to be crowned champions will be between six teams.

The Manchester clubs have a three-point lead over champions Chelsea after their 4-0 win at Stoke - Blues boss Antonio Conte challenged striker Alvaro Morata to continue his good form after the Spaniard scored a hat-trick.

Tottenham Hotspur sit fourth after holding on to win 3-2 at West Ham, while Liverpool are up to fifth after a thrilling victory by the same scoreline at Leicester City.

Pep feeling better a year on

Guardiola enjoyed a scintillating start to life as City boss at the beginning of last season, winning his first 10 matches in charge across all competitions.

But, from a four-point lead at the top of the Premier League at the end of September, City fell away to finish 15 points behind Chelsea.

An unbeaten start has City top again this season, with Guardiola saying he feels more comfortable this term after five wins and a draw, despite not matching last year's 100% start from seven matches.

"We have less points than last season now but I think we have more goals and conceded less," he said. "The feeling I think is a little bit better, but it's just September."

Their hammering of Palace made it 11 goals in two Premier Leagues games, with Raheem Sterling netting twice at Etihad Stadium in addition to strikes from Leroy Sane, Sergio Aguero and Fabian Delph.

Did you know? This is Manchester City's best goal return after six league games (21) and they are the first side to score 5+ goals in three consecutive top-flight matches in the same season since Blackburn did so in 1958-59.

Six teams for the title?

Going into this weekend's games, City and United were level at the top with identical records of points, wins, goals scored and goals conceded.

United lost ground on their fierce rivals in terms of goal difference, but their 1-0 win at Southampton pleased Mourinho because of its hard-fought nature.

Romelu Lukaku scored in his sixth successive league game in the first half, only for Saints to improve in the second and have chances to take a share of the points.

"Last season on this type of fixture we would have given away maybe five or six points, so we are better," said Mourinho, who claimed he did not know why he was sent to the stands by referee Craig Pawson late on.

"It's just the beginning. I think six teams are going to fight for the title."

Did you know? Sixteen points from their opening six games is United's best start to a Premier League season since 2011-12.

Conte challenges Morata

Since defeat at home by Burnley on the opening day, Chelsea have won four and drawn one in the league to sit third.

On Saturday, Morata scored three in the comfortable defeat of Stoke to take his tally for the season to six - level at the top of the Premier League scoring charts with Lukaku and Aguero.

Morata, signed as a replacement for Diego Costa, was tasked by Conte with repeating his scoring feats over the course of the season.

"Morata played a good game," said the Italian. "It was a really good performance. Now he has to continue this way to be a great striker."

Chelsea host Manchester City at Stamford Bridge next Saturday at 17:30 BST.

"I think we have to be focused at what we do and not others," added the Italian. "We want to fight in every competition we are playing."

Did you know? No player has been involved in more goals in their first six Premier League games for Chelsea than Alvaro Morata (eight; six goals, two assists)

'I am in love with Harry Kane'

Spurs were 3-0 up after two goals from Harry Kane and one from Christian Eriksen, but saw Serge Aurier sent off for two yellow cards and had to withstand a late Hammers rally at London Stadium.

Manager Mauricio Pochettino praised Kane, who has been the leading scoring in the Premier League in the past two seasons.

"I find it hard to find the words to describe him," said Pochettino. "I am in love like the fans are in love, like his team-mates are in love," said the Argentine.

"He is so humble, he keeps all the values that managers like me appreciate a lot. That is why I am in love with him for different reasons."

Did you know? Kane has the best minutes-per-goal record in Premier League London derbies of any player to score 10+ goals (112.6 - 21 goals in 29 games).

'This is proof we are still here'

After their 5-0 humbling at Manchester City and last Saturday's frustrating 1-1 draw against Burnley at Anfield, Liverpool got their season back on track at the King Power Stadium.

Goals from Mohamed Salah, Philippe Coutinho and Jordan Henderson secured a 3-2 victory as Simon Mignolet saved a Jamie Vardy penalty.

"I think we really deserved the win," said Klopp. "In a moment like this so many things are positive. The three points are the proof for the public that we are still here, everything is good. Let's make the next step together."

Mignolet, who atoned for fouling Vardy by saving the England striker's spot-kick, added: "We showed character to get through the game and I think this is a big step forward."

Did you know? Liverpool have conceded 10 goals in their past three Premier League away games; the most the Reds have ever conceded over a three-match period on the road in the competition.