It was a lively start to the fixture with the home side surging upfield in their first attack to hit the post. Barkley found Calvert-Lewin who at a tight angle struck the base of upright, before Lukaku failed to pick up the rebound.
Despite the early warning, Chelsea broke out to create danger. Conte's men, well aware that this fixture was probably the most complicated in their run-in, went forward well to put pressure on the Toffees.
Hazard and Costa had chances to put them ahead, while Lukaku also saw opportunities come his way to take the lead. Everton, however, looked mostly off pace as the visitors piled on attack after attack.
The first half transitioned from better to worse, after the excitement from the first twenty-five minutes slowly dissipated towards the end of the half.
Chelsea were beginning to grow impatient as time went by and the initial surge had quelled. In the 66th minute, Pedro picked up the ball 25 yeards out, turned to his left foot and let fly an unbelievable strike into the top corner, away from Stekelenburg's reach. The goal came at a crucial point of the match and may well be worth the title as the catalyst in this match.
Chelsea were still celebrating, while Everton attempted to equalise, when the Blues grabbed a second. Hazard whipped a low cross into the box and Stekelenburg palmed the ball onto Cahill's leg, for the rebound to find the back of the net.
The bad news for Chelsea came as David Luiz limped off to make way for Nathan Ake. The Brazilian defender looked to be holding his groin and Conte will have to wait to see the extent of his injury.
The Italian manager rested key players Hazard and Pedro, and he brought on subs Fabregas and Willian, who linked up for the Brazilian to score the third goal for the league leaders and wrap up the match at Goodison Park.
Chelsea move seven points ahead of Tottenham, and will watch as Spurs host Arsenal in the north London derby. The way Conte celebrated the win at the end you know of its importance. Middlesbrough (H), West Brom (A), Watford (H) and Sunderland (H) are the fixtures remaining for the Blues.