The forward completed the full game while his counterpart was withdrawn after the hour mark.
Key Moments
Two assists from Semenyo's long throw-ins led to strikes by Brooks and Kluivert.
Cole Palmer and Enzo Fernandez found the net for Chelsea in a frantic first half.
Enzo Fernandez missed the best opportunity of a goalless second period.
Bournemouth forward Antoine Semenyo, reportedly close to a big-money transfer, was at the heart of the action, providing two assists and conceding a penalty in a dramatic 2-2 stalemate against Chelsea.
Despite being on the verge of a lucrative switch, the 25-year-old attacker started for his club. He utilized his long throw expertise to great effect, creating scoring opportunities that were finished by Brooks and Kluivert.
Brooks opened the scoring just six minutes in, converting from close quarters after a dangerous long throw from Semenyo.
The home side equalized and went ahead following a foul by Semenyo on Estevao in the box. The match official awarded a penalty after a review by the Video Assistant Referee system.
Palmer calmly dispatched the penalty, placing it perfectly into the corner even though the keeper dove the right way. Fernandez made it 2-1 with a stunning strike into the top corner midway through the first half.
Kluivert leveled the scores again shortly after, tapping home from another precise long throw delivered by Semenyo.
Chelsea created further opportunities, but Bournemouth ended the first half strongly, testing goalkeeper Robert Sanchez with numerous attempts.
The home side's boss reshuffled his team at the break, bringing on James and Neto for Acheampong and Garnacho.
Early in the second half, a handball appeal against Malo Gusto was dismissed by the VAR official. Former Chelsea goalkeeper Djordje Petrovic then produced an excellent save to deny Estevao from distance.
The best chance of the second half fell to Enzo Fernandez in the 77th minute, but he blazed his shot over the bar from inside the box.
Moments earlier, Palmer was substituted for Joao Pedro, a change that was met with disapproval from some home supporters. Although they enjoyed more possession late on, the hosts were unable to craft a winning goal.
In injury time, Bournemouth substitute Enes Unal volleyed over from 12 yards out after a cross from Amine Adli.
The result means Chelsea have managed just one victory in their last seven league outings. Bournemouth's winless streak now stretches to ten matches across all competitions.
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