Chelsea were the better of the two sides during the opening 45 minutes, but a Josh King double and goals from David Brooks and Charlie Daniels gave the Cherries one of the most famous results in their history.
Bournemouth now sit in 10th place in the standings but Chelsea - who have now failed to score in three successive away games for the first time since 2002 - sit in fifth position after dropping behind Arsenal on goal difference.
Both teams started brightly on the South coast, but Chelsea soon began to establish some dominance and came agonisingly close to taking the lead in the seventh minute when Artur Boruc somehow managed to tip Mateo Kovacic's header from close range onto the crossbar.
Chelsea remained in the ascendancy with Eden Hazard seeing a 20-yard strike well dealt with by Boruc, and it took until the 21st minute for Bournemouth to register their first shot with Andrew Surman firing over from distance.
Pedro should have done better at the other end when cutting inside onto his left foot and only shooting straight at Boruc, and Bournemouth finally began to threaten after the half-hour mark with Brooks heavily involved.
The Wales international failed to convert from 10 yards before seeing a weak header easily saved by Kepa Arrizabalaga, and the playmaker fared no better with a 25-yard strike after a run from the halfway line.
Cesar Azpilicueta attempted to hit back for Chelsea and had a left-footed effort tipped away by Boruc, before a Bournemouth counter-attack ended with Junior Stanislas drilling a first-time attempt straight at Arrizabalaga.
The action did not let up after the restart and Bournemouth required less than 90 seconds to take the lead. Brooks caught the Chelsea backline napping by making a run in behind from a throw-in, and the summer signing cut the ball back for King to lash a shot into the roof of the net from 12 yards out.
Chelsea rallied after going behind but they were struggling to find any space in a congested final third, with only a long-range effort from Pedro threatening an equaliser.
The visitors then proceeded to gift their hosts a second goal. A mix-up on the halfway line between David Luiz and Antonio Rudiger let in Brooks and, after being played through on goal by King, the Welshman cut inside Luiz before forcing the ball into the bottom corner from 10 yards.
Chelsea were starting to be outclassed by Eddie Howe's men, and it got worse in the 74th minute as Stanislas was played through on goal before teeing up King to send the ball into the top corner of Arrizabalaga's net from close range.
The game was over as a contest, but Chelsea continued to search for a consolation goal with Ruben Loftus-Cheek failing to hit the target from inside the penalty area and Rudiger having a close-range header saved by Boruc.
Bournemouth appeared happy to settle for the three goals, but in the final minute of added-on time Daniels added a fourth for the home side as he stooped down to head Jordon Ibe's cross past a helpless Arrizabalaga.
BOURNEMOUTH (4-4-1-1): Boruc; Clyne, Cook, Ake, Smith; Brooks (Ibe 68'), Gosling, Surman, Fraser (Daniels 92'); Stanislas (Mepham 95'); King
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta, Rudiger, Luiz, Palmieri; Kante, Jorginho, Kovacic (Loftus-Cheek 77'); Pedro (Willian 61'), Higuain (Giroud 65'), Hazard