The hosts led twice, scoring either side of half-time, but were pegged back by Modou Barrow and Gylfi Sigurdsson respectively, the latter grabbing his seventh goal in 11 games. The result puts Bournemouth within touching distance of survival, on 38 points, whilst the Swans still have some work to do on 33.
With Francesco Guidolin still recovering from a virus had kept him away from overseeing two consecutive victories, Alan Curtis was the main man on the touchline as Swansea made two changes, Leroy Fer being introduced to the line-up alongside Barrow.
Swansea get into it after Cherries start stronger
The changes didn't have the required effect, straight away at least, with Bournemouth starting much stronger. They took just three minutes to threaten, Josh King heading over from a Max Gradel cross, but they went even closer shortly after - Andrew Surman's free-kick rattling the post.
Swansea managed to stifle the Cherries for a period after that, even having a penalty shout as Charlie Daniels made contact with the marauding Barrow. Nothing was given though, as the visitors struggled to get a foothold on the game, going behind after 36 minutes.
Bournemouth score, Swansea score, repeat...
Lukasz Fabianski was at fault, failing to properly clear an Adam Smith cross, allowing Max Gradel to capitalise and slot home from inside the area. He wheeled away to celebrate with the medical staff that helped him overcome a long term injury, but the joy didn't last long, as Swansea hit back inside three minutes.
The two men thrust into the side played a part. Leroy Fer was the provider, spraying the ball to Barrow on the right hand side, before the pacy winger cut inside and slotted the ball into the corner of the net.
Half-time quickly followed, giving each set of supporters a chance to take in what they'd just seen, little in the knowledge that they'd witness a repeat of events towards the start of the second half. Bournemouth took the lead once more, only for the Swans to level up shortly after.
Max Gradel was again involved as the Cherries scored within five minutes of the restart, assisting this time around. He carried the ball forward, before shifting it out to Josh King, and it was King's shot from the right that beat Fabianski at his near post.
Sigurdsson continued his good form just past the hour mark though, equalising to make it 2-2. Just like Gradel had, Barrow turned provider, finding Sigurdsson with a low cross. The midfielder kept his head, turning nicely before firing into the top corner.
Cook fries Swansea heads with late winner
It didn't mean anything in the end though, as the Cherries grabbed a winner through an unlikely source in Steve Cook. Alberto Paloschi saw a shot superbly saved by Artur Boruc, allowing the hosts to race up the other end, winning a corner. Matt Ritchie swung it in, Cook rising highest to head in and secure a precious three points with little over 10 minutes remaining.
Swansea couldn't put a dent in Bournemouth's now rigid defence in the final period, but now have a fairly inviting chance to put things right, as they host bottom of the table Aston Villa next Saturday.