Jurgen Klopp’s side needed to win their final three games of the season to break Manchester City’s record of 100 points set in 2018.
They were on course when Sadio Mane opened the scoring with a clinical finish from Andrew Robertson’s cross at the Emirates Stadium.
But two careless mistakes condemned Liverpool to a third league defeat this season.
Virgil van Dijk’s wayward backpass went straight to Alexandre Lacazette, who rounded Reds keeper Alisson Becker to slot home in the 32nd minute.
Alisson was guilty of an equally costly blunder when his pass out was intercepted by Lacazette and he picked out 20-year-old Reiss Nelson for a cool close-range finish.
Liverpool have failed to win three of their five matches since clinching the title.
They have 93 points and with just two games left and can only reach 99 at the end of their first title-winning campaign for 30 years.
Arsenal climb to ninth place as they chase qualification for the Europa League.
Mikel Arteta’s side go into Saturday’s FA Cup semi-final against Manchester City in good spirits after bouncing back from Sunday’s defeat at north London rivals Tottenham.
Manchester City had enjoyed a big win off the field already this week with their appeal to the Court of Arbitration for Sport overturning a two-season ban from playing in European competitions, freeing up Pep Guardiola’s men to play in the Champions League next season.
Guardiola left Aymeric Laporte, Kevin De Bruyne, Raheem Sterling and Riyad Mahrez on the bench against Bournemouth to keep them fresh for Wembley, but City still had too much quality in the form of David Silva and Gabriel Jesus.
Silva has just two more matches at the Etihad after a 10-year City
career and showed why he will be so missed by curling a free-kick in off the underside of the crossbar six minutes in.
Bournemouth had chances to level against a makeshift City defence as Ederson turned Junior Stanislas’s free-kick onto the post.
At the other end, Jesus was ruthless as he wriggled between two weak Bournemouth challenges inside the box before firing into the far corner to score for the third consecutive game.
– Stunning strike –
City finally conceded for the first time in five home games since the restart when David Brooks turned home Callum Wilson’s cross two minutes from time.
“It was a really difficult game. We started well in the first 10 or 15 minutes of the second half but then we had a problem in our build-up,” Guardiola said after his side’s 2-1 win.
Defeat leaves Bournemouth still three points adrift of safety from Watford and West Ham, who face each other on Friday.
Wolves remain three points adrift of the Champions League places with just two games to play after Chris Wood’s 96th-minute spot-kick gave Burnley a 1-1 draw at Turf Moor.
It was not until 14 minutes from time that the visitors broke the deadlock thanks to Raul Jimenez’s
stunning strike on the half-volley.
In stoppage-time, Mike Dean pointed to the spot for a handball by Matt Doherty despite the Irishman seemingly being impeded by Wood’s attempt at an overhead kick.
Tottenham won 3-1 at Newcastle to keep their chances of European football next season on track by moving up to seventh.
Harry Kane and Son Heung-min were the key men for Tottenham as the South Korean’s low shot crept in at Martin Dubravka’s near post to
open the scoring.
Serge Aurier started for the visitors just three days after his brother was shot dead in Toulouse and the Ivorian was at fault for Newcastle’s equaliser as Matt Ritchie pounced on a wayward clearance to fire home.
Kane quickly restored Tottenham’s lead with a back-post header and the England captain added a second with his head in the final minute.