Semenyo played the entire match as Palmer was substituted in the second half.
Key Moments
Two assists from Semenyo's long throw-ins led to strikes by Brooks and Kluivert.
Chelsea's goals came from Palmer and Fernandez during a chaotic opening 45 minutes.
Enzo Fernandez missed the best opportunity of a goalless second period.
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.
Brooks opened the scoring just six minutes in, converting from close quarters after a dangerous long throw from Semenyo.
Chelsea responded and then took the lead after Semenyo fouled Estevao Willian inside the penalty area. 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. Enzo Fernandez then extended Chelsea's lead, firing a superb shot into the top corner after 23 minutes.
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.
The home side's boss reshuffled his team at the break, bringing on James and Neto for Acheampong and Garnacho.
A potential handball incident involving Gusto was quickly reviewed and not given by the video officials. Petrovic, once of Chelsea, made a fantastic stop to keep out Estevao's powerful drive from the edge of the area.
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. Despite growing dominance in the latter stages, Chelsea could not find a decisive late goal.
Deep into added time, Unal connected with an Adli cross but sent his volley over the bar from a central position.
This draw extends Chelsea's poor run to only one win in their previous seven Premier League matches. For Bournemouth, the point does little to improve their own form, as they remain without a win in ten games.
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