Match ends, Everton 3, Burnley 1.
Romelu Lukaku scored for a ninth successive home game as Everton beat Burnley to make it eight straight Premier League victories at Goodison Park.
Phil Jagielka scored for the third game in a row as he headed the home side in front shortly after half-time.
But Sam Vokes equalised with a penalty after being brought down by Joel Robles.
Ross Barkley - who endured a difficult week off the pitch - had a key role as Everton regained the lead with a shot that was deflected in via Michael Keane and Ben Mee.
Lukaku's emphatic finish made him the first man to score in nine straight home games for Everton since Dixie Dean in 1934.
The win lifted Everton to fifth place, with Manchester United at home to Chelsea on Sunday and Arsenal at Middlesbrough on Monday night.
Barkley has superb response
Midfielder Barkley was the centre of attention before the match for off-field reasons, having been the subject of a national newspaper column that Everton called "appalling and indefensible".
The club have banned the Sun as a result of Friday's piece by Kelvin MacKenzie, which compared the midfielder, whose grandfather was born in Nigeria, to a "gorilla".
The columnist also wrote that men with similar "pay packets" to Barkley in Liverpool were "drug dealers". The Sun has since apologised for the article and suspended MacKenzie.
Barkley's response was to turn in a superb performance. He was in the right place in the first half to clear Keane's goal-bound header off the line following a George Boyd corner, and played a significant role in Everton's second goal.
The England international collected a Kevin Mirallas pass and weaved in from the left to hit a cross-shot that struck both Keane and Mee before bobbling into the far corner.
He ran to the Gwladys Street End to celebrate - collecting a booking for doing so - but, unfortunately for him, the goal was attributed to Mee.
It was still a day to remember for Barkley, who received a standing ovation when he was substituted towards the end.
Barkley has yet to agree an extension to a contract that runs out at the end of next season, and Everton's fans will hope a new deal can be agreed.
Lukaku proves priceless
Lukaku, like Barkley, faces uncertainty over his future at Everton after failing to agree a contract extension.
Manager Ronald Koeman revealed on Thursday that Lukaku, who is keen to play in the Champions League, has refused to extend a deal that has two years to run.
Yet the Belgium international - nominated for the Professional Footballers' Association's player and young player of the year awards this week - is unaffected by those off-field issues.
He was largely well policed by Keane and Mee, but when he got a chance he was ruthless.
The league's top scorer received a pass from Leighton Baines, spun away from Keane and fired a shot between Tom Heaton and his near post to ensure victory.
Former Everton manager Roberto Martinez, who paid £28m for Lukaku three years ago, suggested during the week that the striker is now worth treble that. With such ruthless finishing, it is hard to argue.
Away-day hope for Burnley
Burnley remain the only team in the Premier League without an away victory this season - yet there was encouragement for them in defeat.
Koeman said the visitors were the better side for the first half-hour, with Keane's header cleared off the line and Vokes denied twice by goalkeeper Robles.
When they went behind to Jagielka's header - turned over the line after Ashley Williams flicked on a corner - they responded instantly.
Robles should take the blame for bringing down Vokes needlessly, but the striker kept his cool to slot in only Burnley's 10th away goal of the season, five of which have been penalties.
Heaton, celebrating his 31st birthday, made several good saves to keep Burnley in it, and they looked good for at least a point as Everton laboured.
The disappointment for manager Sean Dyche would lie in the way they lost their defensive discipline briefly to allow Everton to score two quick goals and seal victory.
Man of the match - Ross Barkley (Everton)
Party like it's 1990 - Everton's home run
- Everton have won eight successive Premier League games at Goodison Park for the first time in the Premier League - their best top-flight run since winning eight in a row between January and April 1990.
- The Toffees have already scored more goals at Goodison Park this season than in their previous 26 top-flight campaigns (41 goals).
- Only one team in Premier League history have had fewer away points after 17 Premier League games than Burnley (Derby - three points in 2007-08).
- There were just 126 seconds between Phil Jagielka's goal and Sam Vokes winning Burnley's penalty at Goodison Park.
- Leighton Baines is the first defender to reach 50 Premier League assists.
- Phil Jagielka has scored in each of his past three games for Everton; as many as he had scored in his previous 71 in the Premier League.
- Ashley Williams has himself assisted in Everton's last three Premier League games - he had only recorded three assists in his previous 209 Premier League appearances.
Kevin Kilbane, former Everton winger on BBC Final Score
"I think Ross Barkley handled today's pressure really well. He cleared the ball off the line at one point and generally succeeded in having an influence on the game.
"His manager Ronald Koeman will be impressed with how he's handled the off-the-field distractions this week."
'Ross is just a normal lad'
Everton captain Phil Jagielka, speaking to BBC Sport: "I've known Ross a long time now and nothing fazes him.
"These things can happen. We had an academy day a couple of days ago, and he was part of that.
"He's just a normal lad who wants to play football. I'll give him the goal even though it's gone down as an own goal."
Everton manager Ronald Koeman: "We know all that kind of stuff off the pitch is not the best, but Ross dealt really well with that and showed today he was focused. He showed his qualities in the second half.
"It took 30 minutes to understand what we needed to do today because Burnley were a top opponent. They showed more aggression than we showed. We were lucky not to be down in the first 30 minutes, but the second half was much better.
"The goal now is to give competition to the teams above us. If we finish strong at the end of the season, then everything is possible."
Burnley manager Sean Dyche: "It's a tough one to take, I thought we were good today. We had two cleared off the line and two good chances.
"We've been punished by a bobbly first goal, a bobbly second one and then a great finish from a top striker. It's a good performance on the road that suggests we will get there in the end.
"There's life in performances like that. We've got to take it on now. We do need a margin of luck."
Everton visit West Ham next Saturday, with Burnley at home to Manchester United the following day.
- 17GueyeBooked at 29minsSubstituted forE Valenciaat 45'minutes
- 8BarkleyBooked at 72minsSubstituted forLookmanat 90'minutes
- 11MirallasSubstituted forBarryat 76'minutes
- 19E Valencia
- 13HendrickSubstituted forWestwoodat 86'minutes
- 9VokesSubstituted forGrayat 74'minutes
- 10BarnesSubstituted forAgyeiat 83'minutes
- Mark Clattenburg
- Shots on Target
Second Half ends, Everton 3, Burnley 1.
Attempt blocked. Romelu Lukaku (Everton) left footed shot from the centre of the box is blocked. Assisted by Enner Valencia.
Substitution, Everton. Ademola Lookman replaces Ross Barkley.
Offside, Everton. Ashley Williams tries a through ball, but Romelu Lukaku is caught offside.
Corner, Burnley. Conceded by Ross Barkley.
Attempt blocked. Michael Keane (Burnley) header from the right side of the six yard box is blocked. Assisted by Ben Mee with a headed pass.
Corner, Burnley. Conceded by Mason Holgate.
Foul by Leighton Baines (Everton).
Daniel Agyei (Burnley) wins a free kick on the right wing.
Substitution, Burnley. Ashley Westwood replaces Jeff Hendrick.
Offside, Everton. Enner Valencia tries a through ball, but Romelu Lukaku is caught offside.
Substitution, Burnley. Daniel Agyei replaces Ashley Barnes.
Attempt missed. Ross Barkley (Everton) right footed shot from outside the box is high and wide to the right.
Foul by Gareth Barry (Everton).
Andre Gray (Burnley) wins a free kick on the right wing.
Attempt missed. Robbie Brady (Burnley) left footed shot from outside the box misses to the right following a set piece situation.
Attempt blocked. Joey Barton (Burnley) right footed shot from outside the box is blocked.
Foul by Enner Valencia (Everton).
Joey Barton (Burnley) wins a free kick in the attacking half.