The 33-year-old produced a thumping header to open the scoring as early as the fourth minute, before Danny Ings levelled up the clash later in the half.
Romelu Lukaku restored Everton's lead on the half-hour mark and Eto'o completed his brace on 85 minutes to kill off any hopes of a comeback from the Clarets.
Below, Sports Mole takes a closer look at the events in Lancashire this afternoon.
© Getty Images
On target: 3
On target: 6
Was the result fair?
Overall, yes. You need only glance at the amount of possession that Everton boasted to get an accurate image of what transpired at Turf Moor this afternoon. Burnley did nowhere near enough to salvage anything from this game, and Everton coasted through the second half without ever really needing to move up a gear.
Still winless in the Premier League after nine attempts, and there was very little evidence from Burnley today that they are good enough to stay in the top flight. The pre-season favourites for relegation did little to dismiss that label once again in a performance that will prompt further concern for manager Sean Dyche.
The Clarets looked far better than they have been recently throughout the first half and might have counted themselves slightly unlucky to trail 2-1 at the break, but that momentum was lost somewhere between the half-time whistle and reappearing for the second period.
They never looked like scoring a second until after Everton had scored their third, and Dyche will be worried about a distinct lack of urgency from his side today. It was not good enough, and a massive improvement is necessary if they have designs on preserving their top-flight status.
Everton were far from their best, but did they need to be? No, not against a side that continue to belie their presence in the Premier League.
They took an early lead through Eto'o, and even Burnley's leveller was contributed by an Everton player after Lukaku inexplicably gave the ball away in the lead up to Ings's equaliser.
Overall it was somewhat of a lazy Sunday for the Toffees, whose players emerged unscathed from this one without having to expend much energy.
Sports Mole's man of the match
Samuel Eto'o: On a day when the clocks went back, veteran forward Samuel Eto'o rolled back the years with a decisive performance that helped Everton record back-to-back wins for the first time this season.
The former Barcelona and Chelsea ace did not need long to justify his inclusion in the first XI by thumping a fourth-minute header past Tom Heaton from an excellent Leighton Baines cross.
Despite enduring spells on the periphery of the game after that, Eto'o struck once more on 85 minutes to effectively seal the win by superbly curling past Heaton from outside the box. The 33-year-old still looks at his talismanic best despite his advancing years.
Romelu Lukaku will be kicking himself for offering Burnley a route back into the clash with a first-half error which saw Ings cancel out Eto'o's opener. The Belgium international played a sloppy pass straight to Lukas Jutkiewicz, who found the run of Ings before the young striker rounded Tim Howard for his first Premier League goal.
He atoned for that gaffe by restoring Everton's lead shortly after, but on another day, against another opposition, the mistake may have cost his side dearly.
Andre Marriner had a busy afternoon, booking six players in an occasionally-fierce match at Turf Moor. However, it did look as if he made all the correct decisions, and he had no controversial penalty appeals to contend with. A solid performance from Marriner.
Burnley: It gets no easier for Burnley as the Clarets travel to the Emirates Stadium to face Arsenal on Saturday.
Everton: The Toffees return to Merseyside tonight and will prepare for next Saturday's visit of Swansea City in the coming days.