Semenyo played the entire match as Palmer was substituted in the second half.
Key Moments
Antoine Semenyo's long throws created goals for David Brooks and Justin Kluivert.
Chelsea's goals came from Palmer and Fernandez during a chaotic opening 45 minutes.
The second half's clearest chance fell to Fernandez, who failed to convert.
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.
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.
The home side equalized and went ahead following a foul by Semenyo on Estevao in the box. 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. Enzo Fernandez then extended Chelsea's lead, firing a superb shot into the top corner after 23 minutes.
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.
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.
Moments earlier, Palmer was substituted for Joao Pedro, a change that was met with disapproval from some home supporters. Despite growing dominance in the latter stages, Chelsea could not find a decisive late goal.
In injury time, Bournemouth substitute Enes Unal volleyed over from 12 yards out after a cross from Amine Adli.
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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