Eight days after conceding five at Manchester City, Sean Dyche’s side endured a second chastening afternoon against one of the Premier League’s alpha teams, losing 4-0 at Turf Moor.
Alvaro Morata had a host of chances in the first half and scored the opener in the 22nd minute while Ross Barkley, rewarded for his late equaliser against Manchester United last weekend with a start, and Willian added long-range efforts in the second half.
Substitute Ruben Loftus-Cheek capped one of the best weeks of his career with a very late fourth.
The result lifted unbeaten Chelsea back above Manchester City, who face Tottenham on Monday, and to within two points of leaders Liverpool.
Hazard’s continuing back problem was the headline team news, but Burnley welcomed back winger Robbie Brady 11 months after he suffered a serious knee injury, with the Irishman’s return further delayed by a frustrating hamstring issue.
Burnley began strongly and Chelsea did not get anywhere near Joe Hart’s goal for the first 10 minutes but, when they did, they nearly scored, Morata flicking on Barkley’s shot and Hart tipping it over at full stretch.
Brady shot across goal and wide with Kepa Arrizabalaga stranded after flapping at a Johann Berg Gudmundsson cross but the pressure at the other end was growing.
Willian, playing in Hazard’s position on the left, was looking particularly dangerous and, after shooting straight at Hart, he curled a delicious shot against the far post.
Burnley’s reprieve was short-lived, though, as, a minute later, Jeff Hendrick was caught in midfield and N’Golo Kante fed Barkley, who provided the perfect through ball for Morata to poke past Hart.
Burnley responded well and James Tarkowski headed over from a corner, before Chelsea were forced into an early change when a tearful Pedro was replaced by Thursday’s hat-trick hero Loftus-Cheek.
The home defence simply could not cope with Morata and he should have scored twice in four minutes but shot wide after running through a host of Burnley players then was denied by another fine stop from Hart having been played onside by a dawdling Matthew Lowton.
The half ended with referee Craig Pawson brandishing three yellow cards, the first two after Tarkowski and Morata squared up, with the Burnley defender unhappy at his opponent’s reaction to a strong tackle in the penalty area.
The third was for a dive by Willian in the box, about which the Brazilian continued to protest his innocence after the half-time whistle.
Following a quiet start to the second half, again it was Chelsea who found another gear and, after Morata headed Willian’s cross over, Barkley was allowed too much time and space and drilled a shot from 25 yards into the bottom corner in the 57th minute.
Five minutes later Chelsea added a third as Willian again cut in from the left and this time his right-footed shot was perfectly placed inside the far post.
Substitute Olivier Giroud tried to get in on the act but curled a shot just wide, while at the other end Ashley Barnes was fortunate to get away with a scything challenge on Arrizabalaga that showed Burnley’s frustration.
Hart looked like he had prevented the scoreline becoming any worse with a stunning save to deny Giroud his first of the season, clawing the Frenchman’s header against the bar, but Loftus-Cheek netted his fourth of the week with a deflected strike in injury time.
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Arsenal made six changes for their Premier League trip to Crystal Palace – but goalkeeper Bernd Leno retained his place in goal for the visitors.
The Gunners, seeking a 12th consecutive win in all competitions, recalled Hector Bellerin, Shkodran Mustafi, Lucas Torreira, Alex Iwobi, Mesut Ozil and Alexandre Lacazette following the 1-0 Europa League win at Sporting Lisbon.
The likes of Aaron Ramsey, who captained Arsenal in Portugal, Sokratis Papastathopoulos and Henrikh Mkhitaryan made way as Granit Xhaka again deputised at left-back with both Nacho Monreal and Sead Kolasinac nursing hamstring injuries.
Leno’s place in goal was under threat by the return to fitness of Petr Cech but head coach Unai Emery opted to stick with the Germany international, with Cech among the substitutes.
Palace, yet to score a home league goal this season, made just one alteration as Jordan Ayew came in for Jeffrey Schlupp.
Jurgen Klopp has welcomed an interlude from the crowded fixture list as Liverpool get a full week to prepare for their next assignment.
Liverpool are vying for honours on both domestic and European fronts, contributing towards a hectic schedule in which three fixtures in the span of eight days has been a common occurrence.
However, their early exit from the Carabao Cup means they will not be in midweek action next week, allowing the players – some of whom undertook long-haul trips during the recent international break – a brief respite.
Arsenal await Liverpool next Saturday and the Reds could travel to the Emirates Stadium as Premier League leaders after brushing aside Cardiff 4-1 to go three points clear of Manchester City, who visit Tottenham on Monday.
Klopp said: “We won the game and that’s really good and for us it’s just the next step.
“Now we have time to recover which is the first time for a lot of the boys and they don’t play in three days again. Our international players haven’t had that since I don’t know when, it’s long ago.
“So we will use the time to recover and prepare for the Arsenal game which will be another nice challenge.”
Mohamed Salah opened the scoring against Cardiff while Sadio Mane struck either side of substitute Xherdan Shaqiri’s first Liverpool goal.
Mane feels Liverpool’s feared front trio comprising of himself, Salah and Roberto Firmino are only able to flourish because of the support they receive behind them.
The three frontmen continue to terrorise defences, having bagged 57 league goals between them last season.
But Mane told Liverpool’s official website: “People always talk about the front three – but it’s the team, the work starts behind us. They make it easier, we are lucky boys and score all the time but all the team did their job.”
Cardiff briefly threatened when Callum Paterson halved Liverpool’s lead after 77 minutes with the visitors’ first shot on goal.
Shaqiri and then Mane made the game safe for Liverpool, who enjoyed 80 per cent possession and had 19 attempts at goal in a dominant display as they continued their unbeaten start in the top-flight this season.
“We played very well even though it was a little bit tight in the second half after it went to 2-1,” Mane added.
“It’s part of football. But after that we controlled the game and created many chances. At the end we scored four goals so I think we deserved to win.”