RUI VIEIRA / AP
Liverpool's Georginio Wijnaldum reacts after scoring the only goal of the game against Sheffield United.
Liverpool and Manchester City have put some distance between themselves and the rest of the English Premier League, but both sides had to work hard for it.
Liverpool were pushed, before being gifted a 1-0 win at Sheffield United on Saturday (Sunday NZ time) that maintained their perfect start to the season.
Manchester City were given all they could handle by Everton before two late goals sealed a 3-1 win.
The results mean Liverpool stay five points ahead of City, who are now four points clear of West Ham and five clear of a gang of six teams.
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Liverpool made it seven wins from seven to open the season with a big helping hand from Sheffield United's Dean Henderson.
The Blades' keeper let Georginio Wijnaldum's shot from near the edge of the area squirm through his legs for the only goal at Bramall Lane.
It came on the Reds' first shot on target in the 70th minute, but was enough to settle matters.
"These games, they are not all beauties and you have to work hard for the results," manager Jürgen Klopp told BT Sport.
"They threw everything at us. They worked incredibly hard. They were a real threat.
"I am fine with the game, not overly happy but it happens.
"We didn't play our best football but there we are."
Liverpool's win put the pressure on City as they visited Goodison Park in the day's late match.
And the champions took a first half lead through Gabriel Jesus, only for Dominic Calvert-Lewin to equalize before half-time.
But Riyad Mahrez re-established the lead with a 71st-minute free-kick and Raheem Sterling's late score clinched the win. Elsewhere, 10-man Tottenham beat Southampton 2-1 to move into the European Champions League places.
Tanguy Ndombele gave Spurs a first-half lead before Serge Aurier was sent off for a second yellow card.
A blunder by keeper Hugo Lloris allowed Danny Ings to level, but Harry Kane scored two minutes before the break. The hosts then doggedly dug in in their own half to see out the match.
Meanwhile, coach Frank Lampard finally tasted victory at Stamford Bridge in the league as Chelsea beat Brighton 2-0 with goals from Jorginho and Willian.
It was the Blues' ninth win in nine league games against the Seagulls, an English record for most games won against a single opponent without a loss.
Matt Doherty's score and Daryl Janmaat's own goal gave Wolves their first win and kept Watford rooted to the bottom of the table on two points.
Luka Milivojevic and Andros Townsend gave Crystal Palace a 2-0 win over Norwich and Aaron Creswell's late goal earned West Ham a 2-2 draw at Bournemouth.
Burnley twice came from behind to draw 2-2 at Aston Villa as goals from Jay Rodriguez and All Whites star Chris Wood canceled out scores from Anwar El Ghazi and John McGinn.
Fifth-placed Leicester can pull back within two points of City by beating Newcastle in Sunday's lone match (Monday NZ time).
Manchester United face Arsenal on Monday (Tuesday NZ time).