Manager Sean Dyche enjoyed a winning return to Burnley as his in-form Everton side picked up their fourth consecutive Premier League victory.
Dyche was in charge at Turf Moor for almost 10 years before being sacked last year, and there was no room for sentiment as his Toffees team ruthlessly moved seven points clear of the relegation zone.
James Trafford made a superb save to keep out Dominic Calvert-Lewin's header, but Amadou Onana leapt above the Burnley goalkeeper from the resulting corner to nod in the opener from Dwight McNeil's delivery.
The visitors doubled their lead after 25 minutes as Michael Keane stroked in at the second attempt after his initial effort was saved by Trafford and Dara O'Shea failed to clear the rebound.
Burnley looked to threaten in the second half as Zeki Amdouni forced Jordan Pickford into a fine save at full stretch and Sander Berge rattled the crossbar, but a bleak season continues as the Clarets remain second bottom and are now six points adrift of safety.
Follow live coverage of Saturday's gamesHow did you rate Burnley's performance? Have your say hereWhat did you make of Everton's display? Send us your views hereA win made in Burnley
Dyche took charge of the Clarets for over 400 games and brought them up twice from the Championship, but he was dismissed in April 2022 and the team eventually went down again.
When Everton were deducted 10 points for breaching Premier League financial rules last month, some thought the sanction could destroy morale and result in the team and their manager ending up in the second tier.
Dyche has instead injected fresh impetus into their season and the outstanding form has continued, his players collecting their 10th victory in the last 14 games in all competitions to move up to 16th in the table.
This was their eighth league win of the top-flight campaign so far, matching their haul from the entirety of last season, and that alone highlights the progress they have made under Dyche.
Not only did Burnley's old manager come back to haunt them, but two former Clarets players did too as McNeil - who headed narrowly wide when it was goalless - provided the assist for the opener and Keane scored the second.
Centre-half Keane could have had another in the second half but struck the post from close range, as Everton kept their fourth straight shutout, with only leaders Liverpool and second-placed Arsenal conceding fewer goals than the Blues this term.
More to follow.
Player of the match
PattersonNathan Patterson
with an average of 8.57
Burnley
Squad number1Player nameTrafford
Squad number34Player nameBruun Larsen
Squad number16Player nameBerge
Squad number22Player nameVitinho
Squad number8Player nameBrownhill
Squad number47Player nameOdobert
Squad number2Player nameO'Shea
Squad number17Player nameFoster
Squad number9Player nameRodríguez
Squad number44Player nameDelcroix
Squad number10Player nameManuel
Squad number25Player nameAmdouni
Squad number5Player nameBeyer
Squad number15Player nameRedmond
Squad number28Player nameAl Dakhil
Squad number31Player nameTrésor
Everton
Squad number2Player namePatterson
Squad number5Player nameKeane
Squad number22Player nameGodfrey
Squad number8Player nameOnana
Squad number6Player nameTarkowski
Squad number7Player nameMcNeil
Squad number37Player nameGarner
Squad number11Player nameHarrison
Squad number1Player namePickford
Squad number16Player nameDoucouré
Squad number14Player nameBeto
Squad number9Player nameCalvert-Lewin
Squad number61Player nameDobbin
Line-ups
Burnley
Formation 4-4-2
1Trafford22da SilvaSubstituted forRedmondat 87'minutes2O'Shea5Beyer44DelcroixSubstituted forAl Dakhilat 70'minutes34Bruun LarsenSubstituted forManuelat 82'minutes16Berge8Brownhill47OdobertSubstituted forTrésorat 87'minutes9RodríguezSubstituted forFosterat 45'minutes25AmdouniSubstitutes
10Manuel14Roberts15Redmond17Foster24Cullen28Al Dakhil31Trésor45Obafemi49MuricEverton
Formation 5-4-1
1Pickford2Patterson22Godfrey5Keane6Tarkowski7McNeil11Harrison16DoucouréSubstituted forDobbinat 45'minutes8Onana37GarnerBooked at 82mins9Calvert-LewinSubstituted forGomes Betuncalat 82'minutesSubstitutes
10Danjuma12Neves Virgínia14Gomes Betuncal28Ramalho Chermiti31Lonergan58Hunt61Dobbin73Campbell86MetcalfeReferee:Anthony Taylor
Attendance:21,413
Live Text
Match ends, Burnley 0, Everton 2.
Second Half ends, Burnley 0, Everton 2.
Foul by Nathan Redmond (Burnley).
Amadou Onana (Everton) wins a free kick in the attacking half.
Attempt missed. Mike Trésor (Burnley) right footed shot from outside the box is high and wide to the right. Assisted by Josh Brownhill.
Attempt saved. Beto (Everton) left footed shot from the left side of the six yard box is saved in the centre of the goal. Assisted by James Garner with a through ball.
Corner, Burnley. Conceded by Dwight McNeil.
Substitution, Burnley. Mike Trésor replaces Wilson Odobert.
Substitution, Burnley. Nathan Redmond replaces Vitinho.
Attempt missed. Lyle Foster (Burnley) header from the centre of the box misses to the left. Assisted by Josh Brownhill with a cross following a set piece situation.
Substitution, Burnley. Benson Manuel replaces Jacob Bruun Larsen.
Substitution, Everton. Beto replaces Dominic Calvert-Lewin.
James Garner (Everton) is shown the yellow card.
Zeki Amdouni (Burnley) wins a free kick in the attacking half.
Foul by James Tarkowski (Everton).
Attempt blocked. Sander Berge (Burnley) right footed shot from outside the box is blocked. Assisted by Wilson Odobert.
Attempt blocked. Sander Berge (Burnley) right footed shot from outside the box is blocked. Assisted by Jacob Bruun Larsen.
Jacob Bruun Larsen (Burnley) wins a free kick on the right wing.
Foul by Dwight McNeil (Everton).
Corner, Burnley. Conceded by Michael Keane.