Eddie Howe’s side embarked on their first ever top-flight campaign widely tipped for a quick return to the Championship, but they seem certain to defy the pundits’ predictions after a thrilling clash at Dean Court.
Max Gradel put Bournemouth ahead before Swansea forward Modou Barrow equalised to become the first Gambian to score in the Premier League.
Josh King restored the hosts’ advantage, then Gylfi Sigurdsson drew Swansea level, only for Cook to win it for Bournemouth with 12 minutes left.
Bournemouth’s third successive win lifts them 13 points clear of the relegation zone on 38 points with eight games remaining.
Given that 37 points was enough points to stay up in each of the last four seasons, Bournemouth should be back in the Premier League next season.
Swansea’s future is less certain after a loss that leaves them eight points above the bottom three.
Swansea head coach Francesco Guidolin had missed his team’s last two matches after the Italian was hospitalised with a chest infection.
Guidolin was still recovering so, although he picked the team after leaving hospital this week, his assistant Alan Curtis took charge again.
Bournemouth were quickly into their stride and King headed just over from Gradel’s cross before Andrew Surman hit a post with a curling free-kick.
Gradel was the game’s most influential figure though and he opened the scoring in the 37th minute.
Lukasz Fabianski made a hash of punching clear when he came for Adam Smith’s cross and Ivorian winger Gradel pounced with a cool finish into the far corner for his first Premier League goal.
Gradel charged towards the Bournemouth bench to celebrate with the medical staff who helped him during his long spell out with a cruciate ligament injury earlier this season.
The visitors hit back two minutes later as Barrow cut in from the right before curling his shot into the far corner for his first ever Swansea goal.
But Gradel was proving impossible for Swansea to subdue and in the 50th minute he drove forward before picking out King, who drove his shot past Fabianski’s unconvincing attempted save at his near post.
Barrow turned provider in the 62nd minute when his cross found Sigurdsson for a smart turn and blistering drive into the top corner for the Iceland midfielder’s seventh goal in his last 11 games.
There was no let-up from the hosts however and they regained the lead in the 78th minute when Cook headed Matt Ritchie’s corner into the roof of the net.
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