With Arsenal not in action until later, and Liverpool playing against Manchester United on Monday (AEDT), City took the chance to apply the pressure to its title rivals.

However, Pep Guardiola's side did not have it all its own way at Etihad Stadium, where Beto passed up a huge chance for Everton early on.

Set up by the impressive Iliman Ndiaye, Beto somehow failed to score with the goal at his mercy.

The most involvement Haaland had in the first half was when his challenge forced Jake O'Brien into heading against his own crossbar, while Ndiaye stung Gianluigi Donnarumma's palms at the other end before a glut of half-chances for City before the break.

But Haaland took his first chance when it came in the 58th minute, planting a towering header home from Nico O'Reilly's floated centre.

Haaland made it 2-0 five minutes later, with a deflected, low finish doing for Jordan Pickford, who twice denied the Norway international his hat-trick in second-half stoppage-time, as City extended its unbeaten run against Everton in the top tier to 17 games.

Haaland has now plundered 96 Premier League goals in just 105 games.

He is all set to smash the record, set by Alan Shearer in the 1995-1996 campaign, for the quickest player to a century of goals in the competition, which currently stands at 124 appearances.

The 25-year-old is already on 11 top-flight goals this season.

Guardiola lauded Haaland but insisted his side couldn't just rely on the Norwegian's insatiable hunger for goals.

"I am really pleased, not just for the incredible threat to the opponent but [that] we found him much more than in the first half. That is really important, when you have these players you have to use them," Guardiola said.

"Erling lives for it. Our delivery of passes has been better and Erling is our key man right now.

"All jokes aside, really pleased, [but] we cannot rely on just him. We need other players. Wingers, attacking midfielders, they have to make a step up and score goals.

"We were not there for the first 15 to 20 minutes. We lacked energy. We played good after the first goal. We had clear chances and we'll take it. A really positive thing for people coming from the bench and the energy is there but it's better to improve while winning games."

Meanwhile, Everton has won just one of its past 36 Premier League away games against sides that finished in the top four the previous season.

"I was quite pleased with lots of the performance. Not pleased with the result. We've come here and put on a good show, up until the first goal certainly," Toffess boss David Moyes said.

"[We] created a couple of chances in the first half. I wanted to try and challenge the likes of City and Arsenal where we can. We've challenged them today, but we've come up a bit short."