Ashley Barnes's late penalty snatched all three points as Burnley ended Liverpool's unbeaten home run with a surprise 1-0 win at Anfield.
Jurgen Klopp's team dictated play for much of the match. Sadio Mane went close with an early header, Xherdan Shaqiri blazed a shot just wide and Divock Origi also forced Burnley's Nick Pope into action more than once in a one-sided first half.
A minute before half-time, Origi crashed a shot against the crossbar after a defensive error by Ben Mee put him clear on goal.
After Trent Alexander-Arnold went close, Klopp introduced Mohamed Salah and Roberto Firmino from the bench on 58 minutes, and Salah immediately brought a fine reflex save from Pope with a low, angled shot.
Mane shot over after being teed up by Salah as the Reds continued to press, while visiting substitute Johann Gudmundsson put a rare chance wide for Burnley after excellent wing play by Dwight McNeil.
Firmino side-footed wide on 72 minutes but the Reds could find no way through and, seven minutes before the end, Alisson brought down Barnes in the penalty area.
The Burnley forward calmly converted the penalty to end the Reds' 68-match unbeaten home record.
Liverpool's first defeat in three years and 273 days leaves them fourth, on 34 points, six points behind leaders Manchester United at the halfway stage of the season.
It was Burnley's first win at Liverpool since 1974 and it leaves Jürgen Klopp's side six points behind leader Manchester United halfway through its title defense, having not scored in four successive games.
"It obviously didn't work out tonight and that's what we have to admit," Klopp said.
"It's obviously my fault."
Frustrations boiled over at the halftime whistle as Barnes reacted angrily to Fabinho appearing to flick out at him, provoking a small melee, but referee Mike Dean only showed the Brazilian a yellow card. Meanwhile Klopp and Burnley manager Sean Dyche had their own heated exchange as they headed down the tunnel.
"I didn't start it, but it's nothing," Klopp said.
While Liverpool is chasing a record-equaling 20th English title, Burnley is trying to stay in the league and it moved seven points above the drop zone.
"We knew if we keep believing we will get something," Barnes said.
"We were growing into the game. We managed to stick to our jobs, slow everything down, and it worked."
Burnley's first league win at Anfield since 1974 lifts them up one place to 16th on 19 points.