Liverpool underlined just how hard it will be to wrench the Premier League title away from them when they started with the two most expensive signings in their history on the bench but still beat Mersey rivals Everton 2-1 on Saturday.

Florian Wirtz, whose fee was an initial club record 100 million pounds ($134.66 million), kicked his heels on the sidelines for an hour while deadline day signing Alexander Isak, whose 125-million fee was a British record, had even less time to impress.

But Liverpool's 'lesser lights' were more than up to the task with Ryan Gravenberch accepting an assist from Mohamed Salah to put his side ahead before Hugo Ekitike, another summer signing, made it 2-0 at a raucous Anfield.

Idrissa Gueye did pull a goal back for Everton but Arne Slot's side held on to make it five wins from five games at the end of a week in which they also kicked off their Champions League campaign with a dramatic 3-2 win over Atletico Madrid.

"You could see how well we can play if we are fresh -- the first 45 minutes, unbelievable, the way we played," Slot said.

"But the second half was more difficult because of Everton, of course, but also because we ran a bit out of energy. But we didn't run out of mentality."

Tottenham Hotspur moved second with 10 points as they recovered from a two-goal deficit at Brighton & Hove Albion to draw 2-2 -- Jan Paul van Hecke's own goal handing them a point.

Manchester United breathed life into their stuttering season when goals from Bruno Fernandes and Casemiro earned them a thrilling 2-1 home victory over Chelsea.

Wolverhampton Wanderers are still seeking their first point of the season after losing 3-1 at home to promoted Leeds United while the gloom deepened at West Ham United where pre-game protests against the club's owners were followed by a 2-1 home defeat by Crystal Palace that left them 18th.

Ange Postecoglou got his first point since taking over as Nottingham Forest manager when his side drew 1-1 at Burnley, and Fulham beat Brentford 3-1 to climb to seventh in the table.

Slot plans to rotate players

Liverpool are already setting a high bar in the defence of their crown but needed to show graft as well as craft to subdue Everton whose manager David Moyes is now winless in 23 visits to Anfield.

Gravenberch struck in the 10th minute when Salah sent a ball over the top and the Dutch international met it on the bounce with a superb finish past Jordan Pickford.

Ekitike then justified his inclusion ahead of the still not fully match-fit Isak with a neat finish from Gravenberch's pass.

One window of hope for Liverpool's rivals so far this season is that they have not been ruthless and when Gueye halved the deficit there were some jitters but the hosts held on.

Afterwards, Slot said he would rotate his side heavily for Tuesday's League Cup clash with Southampton.

Tottenham threw away a 2-0 lead to lose 3-2 at Brighton last season but showed they are made of sterner stuff under new manager Thomas Frank on Saturday.

They looked in trouble as they trailed against the run of play to goals by Yankuba Minteh and Yasin Ayari but Richarlison replied shortly before the interval.

Tottenham's pressure was rewarded when Van Hecke deflected in a cross by Mohammed Kudus in the 82nd minute.

"It was potentially our best performance of the season," Frank said. "What I loved from the players was the mentality."

A frantic first half at Old Trafford got off to the worst possible start for Chelsea when goalkeeper Robert Sanchez was sent off in the fifth minute.

The hosts, with just one victory to their name previously this campaign, made their numerical advantage count, with Fernandes and Casemiro putting United 2-0 in front inside 37 minutes.

Casemiro's dismissal just before halftime evened up the numbers and gave Chelsea a way back into the contest but Trevoh Chalobah's late header was all the visitors could muster as a nervy United held on for a vital three points.

"We start the game really well, in terms of aggression," United boss Ruben Amorim said. "Of course the sending-off helped us but we were in control anyway.

"Since the beginning of the game we wanted to win really, really bad."

Wolves striker Jorgen Strand Larsen said his side were in a tough spot after a fifth successive league defeat.

"Nobody wants to be in this situation but nobody else can complain about it, only ourselves," he said.

Ladislav Krejci gave Wolves the lead but Leeds hit back before halftime with goals from Dominic Calvert-Lewin, Anton Stach and Noah Okafor. Leeds have seven points from five games.

Thousands of West Ham fans marched in protest against the club's board and the mood soured further when Crystal Palace emerged with a 2-1 victory thanks to a winner from Tyrick Mitchell that lifted the visitors into fourth place.

Neco Williams gave Forest an early lead at Burnley but the hosts scored 18 minutes later with a goal credited to Jaidon Anthony, after an error by defender Oleksandr Zinchenko sent the ball into his own net.

Mikkel Damsgaard scored in the 20th minute to put Brentford on the scoresheet at Craven Cottage, but Fulham responded with goals from Alex Iwobi and Harry Wilson, and then an own goal by Ethan Pinnock put the game out of reach.