It was unlucky 13 for the Clarets as Liverpool set a new club record for consecutive top-flight wins.
The 18-time English champions – although never in the Premier League era after last season’s near miss – had never exceeded a dozen victories in a row.
But thanks to a slice of good fortune Jurgen Klopp's men were able to set a new mark courtesy of an own-goal credited to Chris Wood, a Sadio Mane strike and a late Roberto Firmino effort which earned the Brazilian his own footnote in history.
A deflected cross off Wood which flew into the Clarets’ net with just over half an hour gone broke the deadlock after Sean Dyche’s men had asked questions of the European Champions.
And when Mane was gifted a second goal moments later, Burnley were left with too great a gap to bridge in their quest to avoid a second defeat of the campaign ahead of the international break.
It had been back to business for the Clarets' ‘Premier League team’ after their mid-week cup exit, although both widemen were re-deployed as ex-Everton man Aaron Lennon made his first league start for the Clarets since December in the absence of the injured Johann Berg Gudmundsson.
And a positive selection was reflected in an excellent start from the Clarets, who played with a real intensity to take the game to the league’s early pace-setters.
There were only two minutes gone when Matt Lowton played a ball over the top for Wood to get behind the Liverpool defence.
The striker’s first touch was excellent and after turning inside Virgil van Dyk, it took a decent save from Adrian to keep out his low, curling effort.
Liverpool weren’t averse to going long themselves as they countered with a chance for Mo Salah which brought a finger-tip save from Nick Pope as the England man touched Salah’s fierce strike onto the post.
And Salah was denied again by Pope after 20 minutes after a lovely, clipped pass from Jordan Henderson had got the Egyptian in behind Burnley’s back four.
But with the Clarets giving as good as they were getting, the context of the game suddenly changed with a fortunate opening goal for the visitors.
Trent Alexander-Arnold had been fully extended at the other end of the pitch by Dwight McNeil as the Clarets’ winger showed why he has earned his first selection at England Under-21 level.
But when the Liverpool full-back was able to get forward and deliver a speculative cross, the ball nicked off Wood and in a swirling wind gave Pope no chance as it dropped under the bar and into the far corner.
And with the Clarets reeling from that blow they then handed the Reds a second goal just four minutes later.
The mistakes made by Burnley skipper Ben Mee during his lengthy stay at Turf Moor can virtually be counted on one hand, but this time his mis-placed pass proved costly as Roberto Firmino released Mane to race clear and finish in clinical fashion.
The Clarets needed a response and just before the break Ashley Barnes had a sight of goal which he couldn’t convert into his fifth goal of the season as his shot was dragged wide.
It was not to be Barnes’ day as the striker looked to become the first Burnley player to scored in five consecutive Premier League games - and the first since Ray Pointer 67 years ago to find the net in five successive top-flight games.
And it wasn’t easy going for anyone in a claret shirt trying to pierce a Liverpool defence which closed out its first clean sheet of the campaign.
James Tarkowksi, who had been a pillar of strength and poise for the Clarets at the back, went closest with a header over the top from a McNeil corner before substitute Jay Rodriguez had a late chance which Adrian saved well at the second attempt.
But with a two-goal cushion, the visitors were never removed from their comfort zone.
And with 10 minutes to go they again displayed their ruthlessness on the break to confirm the extension of their 100 per cent start.
Firmino released Salah from half-way and then made up the ground to tuck the ball past Pope from the return pass to become the first Brazilian to score 50 Premier League goals on a day of records for the Reds.
Burnley: Pope; Lowton, Tarkowski, Mee, Pieters; Lennon, Cork, Westwood, McNeil; Wood, Barnes (Rodriguez 79). Substitutes: Hart, Taylor, Drinkwater, Hendrick, Vydra, Long.
Liverpool: Adrian; Alexander-Arnold, Matip, van Dijk, Robertson; Henderson (Oxlade-Chamberlain 71), Fabinho, Wijnaldum, Salah, Firmino (Shaqiri 85), Mane (Origi 85). Substitutes: Kelleher, Milner, Gomez, Lallana.
Referee: Christopher Kavanagh