With the Cherries full of confidence, it was perhaps no surprise that the hosts got off to a dream start, taking the lead after just 10 minutes.
An excellent corner from Alex Scott was met by a glancing header from Evanilson, whose effort was inadvertently guided millimetres over his own goal line by ex-Bournemouth midfielder Jefferson Lerma to give the hosts an early breakthrough.
Andoni Iraola’s side should have doubled their advantage just moments later, as an error from Daichi Kamada resulted in a glorious opportunity for Evanilson, but the Brazilian striker blazed the ball over the bar when he ought to have hit the target.
Bournemouth continued to apply pressure on the visitors’ defence and wasted another big chance to net a second goal inside the opening 20 minutes when Rayan steered a header wide when in a great position inside the box.
Dean Henderson was soon called into urgent action to deny Marcus Tavernier, before drama struck around the half-hour mark, as the goalkeeper was adjudged to have fouled Marcos Senesi, resulting in a penalty being awarded.
Eli Junior Kroupi stepped up to take the spot-kick, and he confidently sent Henderson the wrong way to extend Bournemouth’s lead and secure his 12th Premier League goal of the season - the joint-most by a teenager in their debut campaign in the competition.
The Eagles failed to register a single shot before the break, and though they ended that wait in the first minute of the second half, there was no doubt that the hosts were still the stronger side.
Inside the first 15 minutes following the restart, Rayan saw a close-range header float narrowly over the bar, while only a vital block by substitute Tyrick Mitchell prevented Kroupi from bagging himself a brace.
The match was all but over as a contest after 77 minutes, as a perfectly weighted pass from David Brooks was latched onto by Rayan, and he made amends for his earlier misses with a clinical finish into the bottom corner to add a third goal for Bournemouth in front of a jubilant home crowd.
The Cherries are now unbeaten in their last 15 league games and are up to sixth in the table, with an away trip to Fulham next on their agenda.
Meanwhile, Palace drop to 15th place and must now switch their attention to the UEFA Conference League semi-final second leg at home against Shakhtar Donetsk.
Flashscore Man of the Match: Marcos Senesi (Bournemouth)