Chelsea were close to the opener themselves 10 minutes later, counter-attacking expertly as Diego Costa found Eden Hazard running in behind - but he could only hit the side-netting after rounding the keeper.
Chelsea old boy and current Blues' target Romelu Lukaku flashed a shot wide from 25 yards for Everton, before the visitors went up the other end where Diego Costa latched onto a long ball from David Luiz - but he could only fire way over on the volley from yards out.
An intricate Chelsea short corner routine nearly brought the opener in the second period - but Nemanja Matic could not turn home Victor Moses' eventual cross shot.
The deadlock was broken with a moment of magic from Pedro, who turned with the ball on the edge of the box and rifled an unstoppable left-footed drive into the top corner.
Gary Cahill rather fortunately extended the lead when Maarten Stekelenburgcould only parry a low Eden Hazard free kick onto the defender's leg to make it a scruffy 2-0.
A gorgeous third was scored with five minutes to go when Costa fed late runner Cesc Fabregas, who passed square for fellow sub Willian to score with his first touch.
FACTS, STATS, GOALS AND LOLS
Everton kicked off knowing they are guaranteed European football next season – West Brom’s home defeat to Leicester 24 hours earlier meant the Baggies could no longer go into the top seven.
Leighton Baines was making his 350th appearance for Everton since signing from Wigan for £6million ten years ago.
Chelsea’s central defensive trio of David Luiz, Cesar Azpilicueta and Gary Cahill were playing alongside each other for the 30th Premier League match in a row - a run that started with back-to-back defeats against Liverpool and Arsenal!
World cruiserweight boxing champion Tony Bellew, a big Everton fan, was a keen spectator at Goodison Park. He told BBC 5 Live he would happily play for £5 an hour - he might have the punch to replace £100million-rated Romelu Lukaku up front!
Romelu Lukaku’s remarkable run, that had seen him score in nine successive home matches, came to a predictable end. He is still looking for his first Premier League goal against his old club, although he did score twice in last year’s FA Cup quarter-final victory.
Gary Cahill’s clincher also had an air of inevitability over it. He has now scored four times against Everton, his best haul against any opposition, before Willian put the gloss on with a late third.
Everton’s defeat ended their best home run for 27 years – they had won their previous eight matches at Goodison Park.
Conte’s second half subsititions also proved inspired, as Fabregas provided the cross for Willian to make things safe with Chelsea’s third goal - and a defensive steel when they needed it most. This was their first clean sheet in 12 Premier League matches.
BIG PICTURE
Next Fixtures
Everton
06 May: Swansea (A), PL
12 May: Watford (H), PL
21 May: Arsenal (A), PL
Chelsea
08 May: Middlesbrough (H), PL
12 May: West Brom (A), PL
15 May: Watford (H), PL
21 May: Sunderland (H), PL
27 May: Arsenal (A), FA Cup final
DREAM TEAM RATINGS
EVERTON: Stekelenburg 4, Holgate 6, Jagielka 7, Williams 6, Baines 6, Gueye 7, Davies 5, Valencia 6 (Kone 72, 5), Barkley 6, Calvert-Lewin 6 (Mirallas 72, 5), Lukaku 6 Subs not used: Joel, Barry, Lookman, Pennington, Kenny Booked: Idrissa Gueye, Enner Valencia, Dominic Calvert-Lewin CHELSEA: Courtois 7, Azpilicueta 7, Luiz 8 (Ake 82, 6), Cahill 8, Moses 7, Kante 7, Matic 8, Alonso 6, Pedro 8 (Fabregas 82, 6), Hazard 7 (Willian 85, 6), Costa 6 Subs not used: Begovic, Zouma, Batshuayi, Chalobah Booked: Cesar Azpilicueta, Gary Cahill, Eden Hazard, Diego Costa Goals: Pedro, Gary Cahill, Willian STAR MAN: GARY CAHILL
SOCIAL SAYS
WHAT THEY SAID
Chelsea centre-back Gary Cahill: "We get a result, it feels massive, then they [Tottenham] respond. It's been like that every week. You can see from the celebrations, this was like a cup final for us, one of our hardest with the form Everton have been in at home. To win 3-0 is fantastic.
"It was convincing but we had to work hard for it. 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."
Everton boss Ronald Koeman: "We did well, until the 1-0 maybe. After that we had more problems but that was all about their quality, before that we played well and made it tough for them. Maybe we didn't create a lot of chances, but I was happy. Idrissa Gueye played a fantastic game, Hazard was not the player he can be because of the man-marking.
"It is really tough to beat Chelsea. They showed today their belief and their quality. They will be champions. We need to find the motivation to finish the season strongly."