Liverpool dropped points at Anfield for the first time in the Premier League this season as Burnley fought to a 1-1 draw against the champions.
Liverpool dominated for the first hour as man-of-the-match Nick Pope made two world-class saves from Mo Salah and Sadio Mane, but they came either side of Andrew Robertson's brilliant headed opener from a Fabinho cross (34).
But Burnley made Liverpool rue their missed opportunities, levelling through Jay Rodriguez's fine shot on the turn (70), and they nearly grabbed an unlikely winner late on as Johann Gudmundsson struck the bar from 12 yards with Alisson stranded.
- Klopp: It was Liverpool versus Nick Pope
- How the teams lined up | Match stats
- Premier League table | Fixtures | Live on Sky
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The result means Liverpool need eight points from their final three games to beat Manchester City's record points tally of 100 from 2017/18, and three wins to beat their win record of 32. Burnley's fine form continues, moving up to ninth on 50 points, having lost just one of their last 13 Premier League games.
Liverpool: Alisson (6), Williams (6), Gomez (7), Van Dijk (7), Robertson (8), Fabinho (7), Wijnaldum (6), Jones (6), Firmino (6), Mane (7), Salah (6)
Subs: Keita (5), Alexander-Arnold (5), Oxlade-Chamberlain (NA)
Burnley: Pope (8), Bardsley (6), Tarkowski (7), Long (7), Taylor (7), Pieters (6), Brownhill (6), Westwood (7), McNeil (6), Rodriguez (8), Wood (7)
Subs: Gudmundsson (5), Vydra (5)
Man of the match: Nick Pope
How Burnley hung in and took their chance
Liverpool, who had not dropped points at Anfield for 18 months, lay siege on Burnley's goal in the first half and could have gone in 3-0 up, with Pope's heroics getting in the way.
First, the England stopper produced a magnificent acrobatic save to his left to deny Salah's half-volley from 10 yards, before again denying the Egyptian low down after he had wriggled through at close range.
But, from a corner moments later, there was little he could do to deny Robertson's expert header. Going short from the set-piece, Fabinho received the ball central and spotted the defender back post, and Robertson did the rest, guiding his header beyond Pope and into the top left corner from 12 yards.
It should have been 2-0 just before the break, but again Pope denied Liverpool, diving to his right to tip away Mane's fierce left-footed shot having found a yard of space in the box.
The onslaught continued after the break; Firmino, the No 9 without a Premier League goal at Anfield all season, came within inches of breaking that unwanted tag, rolling an effort onto the foot of the post from the left of the box after Salah had fed him.
Neco Williams was the next to go close after being released by Salah on the left, lashing his effort at the near post into the Kop, before Salah himself miscued with most of the goal to aim at as the ball rebounded to him quickly 15 yards out.
Liverpool made four changes from the side that beat Brighton 3-1; Jones, Mane, Fabinho and Robertson came in, replacing Alexander-Arnold, Oxlade-Chamberlain, Keita and the injured Henderson.
Burnley made just one change after the 1-0 win at West Ham; Chris Wood came in for Matej Vydra up top.
Despite Liverpool's dominance, there was still only one goal in it, and the hosts were kicking themselves with 20 minutes to go as Rodriguez equalised. James Tarkowski beat Fabinho in the air from a deep free-kick, and Rodriguez's brilliant turn and finish from just inside the box found the bottom-left corner.
Burnley had by far the best chance of the closing stages as Alisson flapped at a cross, giving Gudmundsson the chance to put the visitors ahead from 12 yards, but the sub saw his effort crash off the crossbar.
Liverpool did not look on the beach - they were intense and creative for three-quarters of this contest - but Burnley and Pope in particular deserve huge credit for hanging in the game to grab a much-needed point in their quest for an unprecedented European spot.
What the managers said...
Liverpool boss Jurgen Klopp: "It was a good performance in most parts of the game. There were moments when it was Liverpool against Nick Pope. It's hard to create against a team so organised but we created super chances.
"There was always one guy who wanted to deny us and it was Nick Pope. The game left the result open for Burnley. There were corners where Ali was under pressure from those around him and they were always a threat from set-pieces.
"I'm fine for the performance for 80 minutes and it was probably one of our best games against Burnley, but we couldn't get a second and that's why we've been left with a point."
Burnley boss Sean Dyche: "I'm very pleased, considering we hardly got into the game in the first half. We just about hung in there with the goalkeeper making a few saves. At half-time, I said even top sides find it hard to maintain that level for an entire game. I thought we were a threat from set-pieces all day and we took our chance.
"I thought Popey was excellent apart from he had his shoes on the wrong feet because of his kicking. His job is to keep the ball out of the net and he does that very well. I thought the substitutes helped us grow into the game. Jay Rod is a great pro and he chips in with a number of important goals."
On Pope: "He's been performing well all season. One of his biggest strengths is when he makes a mistake, he just gets on with it. He's unorthodox in the sense that he makes saves you wouldn't expect him to make. He's well protected by his defenders and he's respectful of those in front of him too. We've built a mentality and a resilience over some time."
Liverpool are now unbeaten in 58 Premier League home games - however, this draw ended their top-flight record run of 24 consecutive victories at Anfield.
Liverpool had 23 shots in this match, their most in a Premier League game they failed to win since December 2017 (23 vs Everton).
Burnley's Jay Rodriguez has scored in back-to-back Premier League games for the first time since April 2018. Indeed, Rodriguez has been involved in a goal in each of his last four Premier League games (3 goals, 1 assist).
Liverpool's Mohamed Salah had as many shots as the whole Burnley team in this match (6) and twice as many on target (4), but failed to find the back of the net.
Champions Liverpool now travel to Arsenal on Wednesday at 8.15pm, live on Sky Sports, while Burnley host Wolves at 6pm on the same day in the Premier League.