In just the second minute, Burnley opened the scoring with ease, as Sam Vokes scored his first Premier League goal to put the hosts ahead at Turf Moor.
Andre Gray doubled the lead before the break and the Reds failed to respond as they slipped to defeat on a forgettable afternoon in East Lancashire.
Reds behind early on after defensive errors
Jurgen Klopp's Liverpool squad looked weak throughout the match, and within two minutes of kick-off, already found themselves down 1-0.
Vokes slammed beyond Simon Mignolet from the edge of the box after Nathaniel Clyne had been dispossessed.
Despite falling behind, Liverpool kept on and in the 8th minute, Daniel Sturridge had their first real chance only to see his shot was blocked. Adam Lallana had a follow-up attempt, but his shot was also blocked.
Philippe Coutinho - pivotal in last weekend's opening win away at Arsenal - soon had a chance too, but his shot from outside-of-the-box was too high to trouble Tom Heaton.
Chances kept coming for Liverpool, but very few really troubled Burnley, Coutinho wasting another chance by firing wide to the left after 16 minutes.
Another close attempt came in the 29th minute when Sturridge had an attempt which came close, but ultimately went wide to the left.
Gray doubles the home side's lead
But in the 37th minute, Burnley made it 2-0 as Andre Gray found the back of the net from the outside of the box to double the hosts' advantage after debutant Steven Defour's set-up.
Liverpool continued to dominate possession, but they struggled to create clear chances as Burnley defended well.
Klopp opted to make changes with Sturridge subbed off in the 65th minute, before captain Jordan Henderson received a yellow card for a bad foul.
Klopp and co. struggle to respond in poor second-half
Burnley nearly made it 3-0 in the 66th minute, on a shot that once again went wide to the left, while Liverpool peppered the Burnley goal with shots from distance.
Coutinho and Roberto Firmino forced saves from Heaton, while Marko Grujic's first involvement after being subbed on was to test the 'keeper with a good attempt, but they couldn't find a way back in to the game.
Even the stats showed that Liverpool boasted 81% possession overall, attempting 24 shots, but they managed only five on target - whereas Burnley scored twice from their three shots.
Now, Klopp will be keen to ensure his side respond positively in their next match away at Tottenham Hotspur, while Burnley take on Chelsea.
Liverpool had the higest possession figure for a losing side in the Premier League since the 2003-2004 season (80.6%)
With the win, Burnley enjoyed their first league victory against Liverpool since 1974. Prior to that, they had gone seven matches without a win against Liverpool.
Burnley scored more goals in the match than they had in seven previous home Premier League games.
Sam Vokes scored his first Premier Leauge goal in his 28th top-flight appearance.
Liverpool have only registered one clean sheet in their past 11 away Premier League games.