Liverpool looked to have done enough to win after Divock Origi put them 2-1 up, but Bournemouth punished slack defending to salvage a point and leave the Reds' chances of stealing second place from Spurs looking bleak.
The last meeting between the two teams in December was even more dramatic, resulting in an incredible 4-3 Bournemouth win after Liverpool led 3-1 and Eddie Howe's side looked set to provide stern opposition once again, as they raced into an early lead when Benik Afobe capitalised on an awful Georginio Wijnaldum error.
Liverpool did eventually restore parity five minutes before half-time, though, as Philippe Coutinho scored his 29th Premier League goal to go level with Juninho as the division's most prolific Brazilian.
The hosts were well on top following the interval and, after Nathaniel Clyne saw a brilliant long-range attempt come back off the crossbar, Wijnaldum made amends for his earlier mistake and set up Origi to complete the turnaround with 59 minutes played.
But Bournemouth were afforded more possession in the final 15 minutes as Liverpool sat back and Howe's side took full advantage, former Manchester United youngster King slamming in with three minutes to go to continue his impressive run of form.
A minute's applause ahead of the 28th anniversary of the Hillsborough disaster on April 15 preceded kick-off and the atmosphere created by that had Liverpool looking amped up early on.
So fired up were Liverpool that they went close to opening the scoring inside the first minute, as Roberto Firmino saw a long-range effort tipped over by Artur Boruc.
But at the back the Reds looked sloppy and gifted Bournemouth the lead just seven minutes in.
Wijnaldum panicked under pressure from Harry Arter and saw his hapless backpass pounced upon by Afobe, who coolly prodded beyond Simon Mignolet.
Bournemouth should have got a second 15 minutes later, but Marc Pugh sent a rasping half-volley agonisingly wide of the right-hand post from six yards.
And Liverpool made the most of that let-off just before the break.
Firmino managed to squeeze a pass through the Bournemouth defence and Coutinho tucked away from 12 yards despite initially struggling to get it under his control.
Liverpool's superiority continued into the second half and they went desperately close to taking the lead two minutes after the restart – Clyne hitting the crossbar with a ferocious 25-yard drive.
But Bournemouth did not get so lucky just before the hour.
Wijnaldum turned Jack Wilshere inside out in the penalty area before then chipping a precise delivery into the danger zone for Origi to head beyond the helpless Boruc.
Bournemouth refused to lie down and let Liverpool cruise to victory, though.
Ragnar Klavan failed to get in front of King when a long throw troubled Liverpool and the Norwegian sent a fierce effort into the bottom-left corner to leave the Reds trailing Spurs - who have a game in hand - by five points.
Key Opta stats:
- Premier League games involving Liverpool this season have seen 105 goals; the most of any team in the division.
- The Reds have won just two points in four Premier League games without Sadio Mane appearing this season (W0 D2 L2).
- Bournemouth have lost more points than any other Premier League team from winning positions so far during this campaign (20 – level with West Ham).
- Josh King has doubled his Premier League goal tally from last season (6) with 12 goals, scoring nine goals in his last 10 Premier League appearances for the Cherries
- Roberto Firmino is the first Liverpool player to assist in three consecutive Premier League games at Anfield since Luis Suarez in February 2014.
- 13 of Roberto Firmino's 15 goal involvements this season have come at Anfield (7 goals, 6 assists), including each of his assists.