The Clarets were unable to spoil Carlo Ancelotti’s welcome party as a late goal from Dominic Calvert-Lewin gave the Italian a winning start on Merseyside.
The three-time Champions League-winning manager has been hired to mastermind a revival on the blue side of Stanley Park.
And despite the best efforts of a dogged Burnley side, Ancelotti saw his side put his first three points on the board as the Clarets’ back line was finally breached for the first time in more than four-and-a-half hours.
No team has kept more Premier League clean sheets this season than the Clarets and Sean Dyche’s men were less than 15 minutes away from their eighth of the campaign when they were finally undone by Calvert-Lewin’s flying header.
Burnley - with Kevin Long on as an extra attacking presence - could find no response as they looked to avenge the Boxing Day defeat of 12 months earlier.
But while that 5-1 beating was a low point, this was no give-away as the Clarets made Everton fight all the way to give their high-profile boss the perfect Christmas gift.
Ancelotti was given a predictably rapturous welcome before kick-off at a buoyant Goodison Park where the mood might have been dampened by an early Burnley goal.
It took a timely headed interception from Yerry Mina to snuff out that possibility as Chris Wood waited to nod in a header back across from goal from Jay Rodriguez, starting in place of Ashley Barnes following his late winner at Bournemouth last Saturday.
That near opening came from a Clarets’ free-kick and set-pieces were the dominant feature of a first half dominated by the Merseysiders - who had been unbeaten in three league games under caretaker boss Duncan Ferguson - without a goal to show for it.
The deliveries of Gylfi Sigurdsson constantly asked questions which the Clarets managed to answer, although it took a superb early save from Nick Pope to keep out a close-range effort from Calvert-Lewin after Mina had again won the ball in the air.
Pope’s assured handling helped eased the pressure, although it was another big save with his right foot that denied Everton for a second time before the break as he did well to keep out a skidding effort from Djibril Sidibe.
The Clarets’ use of set-plays was also their major weapon and Wood will have been relieved to have found out at half-time that he was fractionally offside – according to the television pictures – when heading an Ashley Westwood free-kick over the bar when he looked a near certain scorer.
Everton continued to press at the start of the second half but they were having things less and less their own way as the Clarets saw more of the ball and began to sense they could grab something on the break.
Robbie Brady – starting in place of the suspended Jeff Hendrick – swapped flanks with Dwight McNeil and when the two combined, Brady wasn’t far away with a decent heading chance from McNeil’s cross before making way for the returning Johann Berg Gudmundsson.
The Icelander hadn’t figured since the Clarets’ home win over Everton at the start of October due to injury.
But rather than try and conjur up an opening goal, his quest became to try and help find a late equaliser once the Toffees struck to get their noses in front 10 minutes from the end.
Pope and the Clarets’ back four had been superb, with the central pillars of Ben Mee and James Tarkwowski again outstanding.
But when McNeil mis-placed a pass and Sidibe was allowed to cross, they couldn’t prevent Calvert-Lewin diving full length to glance his sixth Premier League goal off the season in off the far post and end Burnley’s hopes of a hat-trick of wins.
Everton: Pickford; Coleman, Mina. Holgate, Digne; Sigurdsson, Delph, Sidibe (Walcott 90), Richarlison (Davies 86), Bernard (Kean 77); Calvert-Lewin. Substitutes: Stekelenburg, Baines, Keane, Tosun.
Burnley: Pope; Bardsley, Tarkowski, Mee, Taylor; Brady, Cork (Long 88), Westwood, McNeil; Wood (Barnes 73), Rodriguez. Substitutes: Hart, Lowton, Drinkwater, Pieters.
Referee: Anthony Taylor