Semenyo played the entire match as Palmer was substituted in the second half.
At a Glance
Antoine Semenyo's long throws created goals for David Brooks and Justin Kluivert.
Cole Palmer and Enzo Fernandez found the net for Chelsea in a frantic first half.
The second half's clearest chance fell to Fernandez, who failed to convert.
In the midst of advanced transfer talks, Bournemouth's Antoine Semenyo delivered a mixed performance, setting up two goals and giving away a spot-kick in a thrilling draw with Chelsea.
The 25-year-old, who is in deep discussions over a potential multi-million pound move, nonetheless featured for his current side. His distinctive long throw-ins proved a potent weapon, leading to goals for teammates David Brooks and Justin Kluivert.
The deadlock was broken early when Semenyo's first long throw caused havoc, allowing Brooks to score from close range in the sixth minute.
Chelsea responded and then took the lead after Semenyo fouled Estevao Willian inside the penalty area. Referee Sam Barrott pointed to the spot after consulting the Video Assistant Referee (VAR) monitor.
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.
Bournemouth hit back almost immediately, as another Semenyo long throw was turned in by Justin Kluivert from close range just four minutes later.
Chelsea created further opportunities, but Bournemouth ended the first half strongly, testing goalkeeper Robert Sanchez with numerous attempts.
At halftime, Chelsea's manager made two changes, introducing captain Reece James and Pedro Neto for Josh Acheampong and Alejandro Garnacho.
A potential handball incident involving Gusto was quickly reviewed and not given by the video officials. 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.
Palmer's withdrawal for Pedro was greeted by boos from a section of the home crowd as the manager's side sought control. 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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