The forward completed the full game while his counterpart was withdrawn after the hour mark.
Match Summary
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.
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.
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. 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.
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. Petrovic, once of Chelsea, made a fantastic stop to keep out Estevao's powerful drive from the edge of the area.
Fernandez had the clearest opportunity to win it late on, but he skied his effort from a promising position inside the penalty area.
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.
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.
Renewable energy consultant with over a decade of experience in sustainable development projects across Europe.