LONDON â€” Chelsea passed the toughest test of the title run-in to keep Tottenham at arm's length.
Antonio Conte's side took 66 minutes to break through Everton's resistance on Sunday before winning 3-0 to remain four points ahead of Tottenham.
Even if Tottenham cannot overhaul Chelsea in the final four games to win the title for the first time since 1961, it will still be a landmark season for the north London club.
Beating Arsenal 2-0 in Sunday's derby ensures Tottenham will finish above its neighbour for the first time in 22 years. And if Spurs hold on to second place, it will be their highest finish in 54 years.
For Arsenal, the challenge is now extending the team's 20-year run in the Champions League. But Arsene Wenger's side is six points behind Manchester City, which occupies the fourth qualification place.
City was held 2-2 by relegation-threatened Middlesbrough, but fifth-place Manchester United could also only draw with Swansea so remains a point behind its neighbour.
TOTTENHAM 2, ARSENAL 0
It was the penultimate game at White Hart Lane before the stadium is demolished and Tottenham moves into a new adjacent venue after a season at Wembley.
Arsenal imploded at the start of the second half.
Harry Kane ran onto a long throw-in and held up the ball under pressure from Gabriel Paulista. Dele Alli seized possession and passed to Christian Eriksen, who weaved past Laurent Koscielny before striking at goalkeeper Petr Cech. The shot was parried, but Alli stuck out his left boot into a crowded area to clip the loose ball into the net in the 55th minute.
Arsenal never recovered. It took 77 seconds for the penalty to be conceded, with Kane going down lightly under Gabriel's challenge and winning the spotkick. Kane netted his fifth in five league games against Arsenal.
"I felt that we lacked a little bit freedom to play and desire to hurt them more than what we did," Wenger said.
Arsenal's season could still end with the FA Cup if it beats Chelsea at Wembley Stadium.
Tottenham is now virtually assured of making the top four, given its superior goal difference over fifth-place Manchester United, but manager Mauricio Pochettino still craves the title.
"Of course I am disappointed, because it was a great opportunity to reduce the gap, but we are four (points behind Chelsea)," he said. "But now it's a moment to feel proud, happy."
EVERTON 0, CHELSEA 3
It was worth the 66-minute wait for a goal. Pedro Rodriguez collected the ball on the edge of the penalty area before striking under the crossbar from 25 yards (meters).
Gary Cahill gave Chelsea breathing space in the 79th by bundling the ball into the net after Eden Hazard's low free kick was saved. Substitute Willian completed the victory seven minutes later.
"We have to have great enthusiasm and great patience because I think we are having a great season but to become a fantastic season we must win," Conte said of the title.
MANCHESTER UNITED 1, SWANSEA 1
Jose Mourinho's side made it a club record 25 matches unbeaten but the celebrations were muted after this 14th draw of the campaign.
United captain Wayne Rooney converted a penalty won by Marcus Rashford but Gylfi Sigurdsson equalized directly from a free kick in the 79th minute.
To compound Mourinho's misery, Luke Shaw and Eric Bailly joined a lengthy injury list.
Swansea is two points from safety with three games to go.
MIDDLESBROUGH 2, MANCHESTER CITY 2
Gabriel Jesus made a quick impact on his first start following 10 weeks out with a foot injury, salvaging the draw in the 85th by heading in Sergio Aguero's cross.
Former City striker Alvaro Negredo put Middlesbrough in front before Aguero levelled from the spot. Gabriel Jesus cancelled out Calum Chambers' strike.
Rob Harris, The Associated Press