Junior Stanislas fired a brace to add to goals from Cook, Charlie Daniels, Callum Wilson and Dan Gosling, as Eddie Howe's men romped to their record Premier League victory.
Centre-back Cook gifted Hull possession then clumsily diverted Ryan Mason's speculative effort past the wrong-footed Artur Boruc - before burying a header at the other end just seven minutes later.
Mason's fortunate goal had Hull level at 1-1 and Cook pounding the turf in disbelief
When the Cherries stalwart nodded home Stanislas' free-kick, he relished his quick-fire redemption with a conciliatory wave to the home support.
A dismal showing from Hull leaves Mike Phelan's side without a Premier League win in their last six matches
That this was Phelan's first game as full-time manager after a lengthy caretaker stint made it all the worse.
Bournemouth fired six Premier League goals for the first time amid another assured showing dictated by midfield marshal Harry Arter.
The 26-year-old picked the right day to conduct the tempo, with Ireland boss Martin O'Neill no doubt an impressed spectator.
Cherries manager Howe's possession-based blueprint owes everything to link men Arter and Andrew Surman, the two deep-lying midfielders a constant outlet for their team-mates.
Bournemouth immediately hit their attacking straps, the relentless Arter kick-starting every fluid move.
Stanislas curled a free-kick off a post and Daniels buried the follow-up to hand the hosts the ideal start.
Hull spent the next 25 minutes chasing shadows as Eddie Howe's possession play took hold, Jordon Ibe growing in confidence if not end-product.
Half-chances unconverted could have cost the Cherries however, with Wilson striking the bar after diverting Ibe's low cut-back.
Stanislas saw a low drive deflected wide and Ibe blasted over from 25 yards after being left in acres of space once too often.
Just when Bournemouth looked to grapple total control, though, one mistake proved costly
Cook conceded possession far too cheaply with a stray pass, and Hull pounced.
Another Cook blunder gifted the visitors the goal too, the defender lazily redirecting Mason's long-range shot past the blameless Boruc.
The distraught Cook punched the turf then buried his face in his shirt - but somehow found a rapid redemption.
Just seven minutes later the 25-year-old headed home Stanislas' whipped free-kick, relishing the goal and also raising both hands in apology to the home faithful.
Bournemouth's dominance was then fully realised when Robert Snodgrass crudely upended Callum Wilson in the Hull box.
Stanislas stalked the ball from his team-mates once the cast-iron penalty was awarded, and duly converted the spot-kick, firing straight down the middle.
After the break Hull were perhaps unfortunate not to win a penalty when Mason went down under Surman's challenge
But after that the visitors were unable to generate any tangible threat.
Stanislas massaged the scoreline with his second and Bournemouth's fourth goal, tapping in at the far post after an accurate low cross from Adam Smith.
Wilson headed in the fifth, before Gosling curled home the sixth, heaping the indignity on hapless Hull.
Source : PA