Antonio Conte’s side had to work hard to break down Everton’s stubborn resistance, but Pedro’s majestic second-half goal put Chelsea on course for a fourth win in their last five league games.
Late goals from Gary Cahill and Willian wrapped up the victory. Chelsea’s steely display ensured the destiny of the title remains in their hands with four matches left against Middlesbrough, West Bromwich Albion, Watford and relegated Sunderland.
Chelsea need nine points to be assured of being crowned English champions in Conte’s first season in charge.
“We had a lot of patience for the right moment to hit. We deserved the win,” Conte said.
“We scored an amazing goal with Pedro. This gives us lots of confidence. Now it is important to prepare for the final rush. We must look step by step.”
After defeats against Manchester United and Crystal Palace raised questions about their ability to get over the finish line, Chelsea have been revitalised by their FA Cup semi-final win over Tottenham.
They beat Southampton in midweek to re-establish control of the title race and ending Everton’s eight-match winning streak at home was another significant step towards the title.
Restoring Pedro to the starting line-up in place of Cesc Fabregas, Conte put the emphasis on attack, but the leaders were nearly caught cold at the back in the opening minutes.
Dominic Calvert-Lewin wriggled free for a shot from a tight angle that deflected onto a post and rebounded to Romelu Lukaku, whose close-range strike was goalbound until Cahill came to the rescue with a block.
In need of inspiration to break down obdurate Everton, Conte’s men went close early in the second half when a clever short corner routine set up Victor Moses for a shot that was deflected wide.
But Chelsea kept probing and their persistence was rewarded with Pedro’s thunderbolt in the 66th minute.
A sustained period of Chelsea pressure pushed Everton deep into their own penalty area and when the ball was worked to Pedro in a central position the Spanish winger uncorked a fierce 20-yard strike that flashed into the roof of the net for his first goal since February.
With 11 minutes left, Hazard’s low free-kick was pushed out by Stekelenburg and Cahill tapped in to trigger chants of “Tottenham, we’re waiting for you” from Chelsea’s jubilant fans.
There was still time for Willian to come off the bench and score in the 86th minute.