Liverpool's 68-game unbeaten home run in the Premier League came to an end as Ashley Barnes fired in a late winner from the penalty spot to secure a famous victory for Burnley.
Barnes was tripped in the box by goalkeeper Alisson with seven minutes remaining and converted the spot-kick as Burnley won at Anfield for the first time since 1974.
Liverpool's last league loss on their own ground came nearly four years ago, against Crystal Palace in April 2017, and they are now six points behind leaders Manchester United at the midway point in the campaign.
Divock Origi was given his first start of the season and should have scored when he ran free on goal after pouncing on Ben Mee's error but struck the crossbar.
The hosts pushed to find the net in the second half but ran out of ideas, Nick Pope making a stunning save to deny Mohamed Salah and fellow substitute Roberto Firmino flicking an effort wide.
Burnley's shock win lifts them up to 16th in the table, seven points clear of the relegation zone.
Reds out of form
Jurgen Klopp said before the game he was "not worried" by his side's poor run, but the latest setback means this has now turned into a real problem for the Liverpool manager.
After 19 games, Liverpool are out of form and out of confidence, failing to find the net in their last 440 minutes of top-flight action and awaiting their first league victory of 2021.
They looked to be hitting their stride on 19 December when they took apart Crystal Palace 7-0, but have not won in the league since and scored just a solitary league goal in that time, against relegation strugglers West Brom.
Their drop-off from the same stage last season is extraordinary - after 19 games last term the Reds were 13 points clear at the top with 55 points, but they have 21 fewer points now.
Aside from Pope's save to thwart Salah and stops from Origi and Trent Alexander-Arnold, Liverpool did not look a side who were threatening to find the net.
They had 72% possession but much of it was slow and ponderous, and although they had spaces out wide and put 30 crosses into the box, the resolute Burnley defenders headed and hacked clear every ball that came in.
Burnley secure famous win
Liverpool won 18 of 19 league games at Anfield as they cantered to the title last term.
Burnley were the spoilers on that occasion - earning a 1-1 draw in July 2020 - and they bettered that showing here with another solid and well-organised display.
Captain Mee had 14 clearances and made two tackles, while centre-back partner James Tarkowski contributed five interceptions and won the ball back four times.
Burnley are a well-drilled outfit and know their limitations, happy to sit back and soak up the pressure before looking to take their chances on the counter-attack.
They had sniffs on the break but were unable to get the final ball right and while Barnes forced an excellent save out of Alisson, the assistant referee's flag would have ruled it out.
They remain the lowest scorers in the league with just 10 goals - level with bottom side Sheffield United - but their defensive solidity means they will always pose a threat, even to the biggest teams.
'We dealt with the basics' - manager reaction
Burnley boss Sean Dyche to Match of the Day: "Performance, we had to work very hard, as you do in these places, be diligent and do your jobs - shape was good, energy was good.
"We had a golden chance, kept searching, but you have to deal with the basics and we did that very well.
"We were close last year, you get a feel of a performance and I said 'you are used to playing against these players, working without the ball, there's always a chance and you have to take it'. Barnsey sticks it in there, gets a toe, it's a penalty and he sticks it away very well."
Goal shy Reds - the stats
This was Burnley's second Premier League win away against the reigning champions (also v Chelsea in August 2017). Indeed, since the 2017-18 season, Burnley are the only side with two away league wins over the reigning English champions.
Liverpool have gone four league games without scoring for the first time since May 2000. The Reds have had a total of 87 shots since Sadio Mane's 12th-minute strike against West Brom, 25 days ago.
This is the first time a Jurgen Klopp side has gone four league games without scoring since his Mainz side did so in the Bundesliga from November to December 2006.
Liverpool have gone five Premier League games without a win (D3 L2) for only the second time under Klopp (also from Jan-Feb 2017).
Liverpool have conceded two penalty goals at Anfield in this season's Premier League (also Sander Berge for Sheff Utd); they had only conceded two penalty goals at the ground under Klopp before 2020-21.
Liverpool had 27 shots without scoring against Burnley, the most they have had in a single league match without finding the net since April 2013 v Reading (28), and most at Anfield since April 2012 v West Brom (30).
Ashley Barnes' penalty for Burnley was his first away goal in the Premier League in 11 appearances on the road, since netting against Watford back in November 2019.
Since the start of last season, no goalkeeper has made more saves against a single opponent in the Premier League than Burnley's Nick Pope against Liverpool (19). Pope has made 14 saves in his last two games at Anfield, including six tonight.
Liverpool have another big game on Sunday against rivals Manchester United in the FA Cup. That game is live on the BBC (17:00 GMT). Burnley travel to Fulham in the same competition on the same day (14:30).