Chelsea secured three points easily at Goodinson Park while Guardiola's men were held to a 2-2 draw against Middlesbrough.
Chelsea looked every inch champions in taking a significant step towards the Premier League title today with victory at Everton, while the Manchester clubs stumbled in the race for the top four. A superb second-half strike by Pedro and late goals from Gary Cahill and Willian stretched Chelsea's lead at the top over Tottenham to seven points as they emphatically ended Everton's run of eight successive home wins.
The 3-0 win by Antonio Conte's relentless side turned the pressure firmly back on Spurs ahead of their derby with Arsenal later on Sunday. Arsenal badly need three points to stay in the race for a Champions League spot, but their hopes were boosted with Manchester City and United both held to surprise draws against relegation strugglers.
Chelsea took time to settle but once Pedro scored their opener -- his first goal in nine matches -- the floodgates opened and they became an irresistible force against their hosts. Cahill's eighth of the season and Willian's beautifully worked third inflicted only Everton's second home defeat of the season.
"It was convincing but we had to work hard for it," Cahill told Sky Sports. "Pedro's goal was special, at times you need a bit of class to open up a team, that's what he did today. I'm buzzing with that, it's a huge result for us."
City had to come from behind twice to draw 2-2 at Middlesbrough and United drew 1-1 at home to Swansea.
City relied on 20-year-old striker Gabriel Jesus to secure them a point in the final five minutes of their game against a Boro side scenting back-to-back wins in the Premier League for the first time since May 2008. Jesus's vastly more experienced strike partner Sergio Aguero had pulled City level at 1-1 with a penalty before Calum Chambers restored the hosts' lead.
A sublime free-kick by Icelandic international Gylfi Sigurdsson gained Swansea a deserved point against United. Sigurdsson's 10th goal of the season, but first in 11 matches, cancelled out veteran Wayne Rooney's contentious penalty in time added on in the first-half when Marcus Rashford made the most out of minimal contact with Swans goalkeeper Lukasz Fabianski.
It will be of little consolation to manager Jose Mourinho that it extended United's unbeaten run to 25 and they have not been defeated at Old Trafford since September 10th last year. Liverpool are third, City fourth and United fifth, with nothing to choose between them.
But Mourinho saw two more defenders depart injured in the impressive Eric Bailly on the hour mark and Luke Shaw in just the eighth minute. "We lost players and we lost points, so yes today was a bad day," Mourinho told the BBC.
"We did not look tired and exhausted, we are tired and exhausted. You cannot isolate the performance out of the context. This is the ninth match of April, it is not human. We have a squad of 22 that is reduced to 13 or 14 players. The players are very tired. At the moment, we cannot walk from the bed to the loo and break a leg."
His Swansea counterpart Paul Clement said Rashford had "deceived the referee" but added the point enforced their belief they could retain their elite status -- they are two points adrift of fourth from bottom Hull with three matches remaining.
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 "chelsea,gary cahill,pedro,swansea,gabriel jesus,marcus rashford,premier league,antonio conte,bbc,wayne rooney,tottenham,luke sha")
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