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.
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.
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.