Manchester City claimed top spot in the Premier League and took a significant step towards the title by coming from behind to edge Everton 3-2 on Saturday.

Ross Barkley’s stunner put hosts Everton ahead in the 11th minute, but Sergio Aguero quickly equalised and a brace from Edin Dzeko secured victory for Manuel Pellegrini’s side despite Romelu Lukaku reducing the arrears.

City now lead previous leaders Liverpool on goal difference – +59 to +50 – and will therefore be practically assured of winning the title if they win their two remaining games.

Chelsea and Liverpool each have opportunities to take over at the summit over the next two days, but if City beat Aston Villa on Wednesday and win at home to West Ham United next weekend, they are unlikely to be caught.

Everton’s defeat, meanwhile, means that Arsenal are guaranteed to finish at least as high as fourth, guaranteeing them a place in next season’s Champions League play-offs.

“It was a really, really big step,” City manager Pellegrini told Sky Sports.

“We won and that is important. The pressure is maybe too high to play your best football. It is not easy to recover from a goal down, but we did.

“The worst thing we can do is think that we have won the Premier League. We have to try thinking from tomorrow about the game against Aston Villa and then we will see what happens.”

Meanwhile, Fulham and Cardiff City were both relegated after defeats in their penultimate games of the season left them unable to reach safety.

Fulham’s 13-year run in the English top flight was ended by a 4-1 defeat at Stoke City, while Cardiff went straight back down to the Championship following a 3-0 loss at Newcastle United.

Both sides’ fates were sealed by fourth-bottom Sunderland’s unexpected 1-0 win at Manchester United, which took Gus Poyet’s side four points above Fulham and five points clear of bottom club Cardiff.

“I’ve never been relegated until today,” said Fulham manager Felix Magath. “I feel very sad. I have to apologise for not managing the situation. The club asked me to come. I tried.”

Goals from Newcastle trio Shola Ameobi, Loic Remy and Steven Taylor sent Cardiff back to the second tier just a year after their promotion from the Championship.

“The realisation that we’re down is one of the most bitter disappointments of both mine and many of the players’ careers,” said manager Ole Gunnar Solskjaer.

Sunderland will effectively be safe if third-bottom Norwich City lose at Chelsea on Sunday after Sebastian Larsson’s 30th-minute goal at Old Trafford condemned United to their 12th league defeat of the season.

“I feel flat. The players were flat and I don’t know why,” said interim United manager Ryan Giggs, whose side have lost seven home league games for the first time since they were relegated to the old Division Two in 1974.

“We’ve had a problem at home all season. It’s not been good enough.”

United’s defeat means that Tottenham Hotspur need only a point to secure sixth place, and with it Europa League qualification, despite having lost 2-0 at West Ham United earlier in the day.

Elsewhere, Andreas Weimann scored twice as Aston Villa won 3-1 at home to FA Cup finalists Hull City, while Southampton striker Rickie Lambert claimed a 93rd-minute winner in a 1-0 victory at Swansea City.