Burnley suffered a second successive home defeat defeat to a Samuel Eto'o-inspired Everton.
Danny Ings gave the Clarets hope with his first Premier League goal to cancel out Eto’o’s early opener for the visitors.
But Romelu Lukaku put the Blues back into the lead inside the opening half an hour before Eto’o wonderful strike sealed the victory late on.
Stephen Ward was handed his first home league start for the Clarets as he was preferred to Ben Mee in Burnley’s only change to the team that began last weekend’s game against West Ham.
Meanwhile, manager Roberto Martínez selected both Eto’o and Lukaku in an attacking-looking Everton line-up.
And the visitors got off to a dream start.
A quick switch of play from the right to the left side was followed by Leon Osman using Leighton Baines on the overlap.
The full-back crossed the ball into the box where Eto’o, who made a late run to the penalty area, headed the ball home off the crossbar from close range to put the Blues in front.
On 13 minutes, Lukaku had his first shot on goal, but didn’t manage to trouble Tom Heaton from distance.
It took Burnley a quarter of an hour to record their first spell of pressure. When they did, though, first Ward and then David Jones both saw their well-struck efforts blocked amidst some desperate Everton defending.
However, the home crowd could start to sense an equaliser coming.
On 20 minutes, Lukaku gave the ball away inside his own half straight to Lukas Jutkiewicz who instantly slipped Ings through on goal.
The England under-21 international needed no further invitation as he cooly rounded off Tim Howard before slotting the ball into an empty net for his first goal since the last day of last season.
And the Clarets were now pushed further forward by the buoyant Turf faithful.
Only two minutes later, Scott Arfield’s drilled effort from just outside the box flew just wide of the post.
It was the visitors, though, who soon restored their lead thanks to a slick, passing combination.
Eto’o and Steven Naismith were both involved on the edge of the box and after Lukaku’s initial strike was well blocked by Ward, the Belgian forward somehow managed to slot the ball into the far corner of the net through a couple of bodies.
Burnley had to begin their search of another equaliser and they did so quickly.
On 33 minutes, Jutkiewicz was simply too strong for Antolín Alcaraz as he turned towards goal, but was unable to test Howard from a tight angle.
Then, right on the stroke of half-time, Arfield tried his luck once more from outside the box, again only just missing the target as the Clarets came off the pitch for the break trailing.
After the restart, Burnley were the first to threaten when Ward’s ball in caused Alcaraz a problem. However, Jutkiewicz, who looked to pounce on the opportunity, couldn’t generate enough power on his header to seriously trouble Howard.
In response, on 59 minutes, Eto’o combined with Lukaku, but the former’s effort was comfortably held by Heaton.
Five minutes later, Ashley Barnes was introduced into the action in place of Jutkiewicz as the Clarets kept looking for an equaliser.
Meanwhile, England international Ross Barkley came on for a substitute appearance for Everton.
And it was the Blues who seemed to control the tempo of the game during a much less eventful second half.
Being a sole goal behind, though, Burnley looked to apply another spell of pressure as the match was slowly drawing to a close.
With less than ten minutes left on the clock, Arfield dragged a shot wide of the post from just outside the box.
But it was at the other end where the outcome of the game was eventually decided.
Eto’o received the ball about 25 yards away from goal, turned rapidly and curled a beautiful strike right into the far corner of the goal for Everton’s third.
Both teams still had their chances late on. Neither Ings nor Naismith could provide a finish, however, after breaking into the penalty area.
Eto’o then had a great opportunity to complete a hat-trick when he lashed onto a loose ball and rounded off Heaton. However, he could only hit the inside of the post on his left foot.
In the end, it was the more lethal finishing by the visitors that proved the ultimate difference between the two sides.
Burnley: Heaton – Trippier, Duff, Shackell, Ward – Boyd (Chalobah 86), Arfield, Jones, Kightly (Sordell 83) – Ings, Jutkiewicz (Barnes 64).
Subs not used: Gilks, Keane, Mee, Wallace.
Everton: Howard – Coleman, Alcaraz, Jagielka, Baines – Naismith, McCarthy, Barry, Osman (Pienaar 82) – Eto’o, Lukaku (Barkley 64).
Subs not used: Robles, Hibbert, Gibson, Bešić, McGeady.
Goals: Ings 20 – Eto’o 4, 85, Lukaku 29
Bookings: Boyd, Arfield, Ward – Lukaku, Naismith
Referee: Andre Marriner
Attendance: 19,927 (3,955)