Mohamed Salah's glaring penalty miss helped Bournemouth climb out of the relegation zone after an excellent win which damaged Liverpool's chances of qualifying for next season's Champions League.
The Reds were brought back down to earth after last week's 7-0 thrashing of Manchester United as the Cherries, who started the weekend bottom, did their survival chances a power of good.
Liverpool were punished for poor defending when the unmarked Philip Billing struck from eight yards for his sixth Premier League goal of the season after fine work by Dango Ouattara.
Virgil van Dijk had a header cleared off the line at 0-0 and substitute Diogo Jota was denied by Neto's fine save before Liverpool won a penalty when the Portugal forward's header was handled by Adam Smith.
But Salah, who became Liverpool's all-time top Premier League scorer with 129 goals last week, blazed the penalty wide much to the delight of Bournemouth's fans.
Jurgen Klopp's side missed the chance to go fourth for the first time this season after a lethargic display.
Liverpool have made strides in recent weeks but this was a step backward for a team who face a mountainous task to stay in the Champions League when they go to European champions Real Madrid on Wednesday, looking to claw back a 5-2 deficit.
Their patchy away form— just three wins in 13 league games on the road —continues to hold them back. "Concerned? Yes, I see it," added Klopp on his side's away performances.
"In the home games we are in the top four but in the away games we are not even in Europe, there is always a reason and our away results is for sure (the reason)."
With next week's home game with Fulham postponed due to the London club's involvement in the FA Cup followed by the first international break of 2023, this was Liverpool's last game on the Premier League stage for three weeks.
They face back-to-back away games at Manchester City (April 1) and Chelsea (April 4) when they return, followed by a home match with leaders Arsenal (April 9). Klopp will hope his side have washed this defeat out of their system by then.
Mohamed Salah took his 21st penalty in the Premier League, with his latest effort his first to completely miss the target (18 scored, 2 saved previously)
