Strikes from Steve Cook, Callum Wilson, Charlie Daniels and a Yann Kermorgant penalty helped The Cherries to equal their club record of 104 goals in a single season.
Blues, who had captain Paul Robinson sent off late on, had looked to be heading for a surprise win when Clayton Donaldson and David Cotterill struck in three first-half minutes.
There was an air of anxiety in the stands around the Goldsands Stadium and that spread on to the pitch as Bournemouth made a nervy start.
Cotterill's 13th shot from the edge of the penalty area looped off Cook and behind for a corner after the latter had been caught in possession.
Wilson then passed up a glorious chance to give Bournemouth the lead a minute later, firing into the side-netting after latching on to Ryan Fraser's low cross.
And Donaldson showed Wilson how to finish in the 19th minute, racing in between the centre-back pairing of Cook and Tommy Elphick before calmly lifting the ball over the onrushing Artur Boruc and into the net.
Cotterill doubled the Blues' lead only three minutes later with another superbly-taken goal.
The Welsh international left full-back Daniels on his backside with a mesmerising jinking run before driving a low right foot shot across Boruc and into the far corner.
Donaldson should have made it 3-0 twelve minutes before half-time, seizing on Cook's tame back header only for Elphick to scramble back and clear the striker's shot off the line.
Cook gave Bournemouth a lifeline in the 39th minute by bundling the ball home from close range after Blues goalkeeper Darren Randolph had flapped at Matt Ritchie's corner.
The Cherries drew level on the stroke of half-time when Harry Arter split the Blues defence apart with a delightful through ball for Wilson to round Randolph and tap into an empty net.
Kermorgant completed the comeback from the spot three minutes after the interval following Robinson's clumsy foul on Wilson.
And home captain Elphick came within inches of extending the lead when his 58th minute header hit the crossbar.
Randolph also saved smartly with his legs to deny Wilson after Bournemouth's top-scorer had been played through by Kermorgant.
Daniels then added his name to the scoresheet 16 minutes from time with a fiercely-struck half volley from the edge of the area which cannoned in off the frame of the goal.
Blues' misery was compounded in the 79th minute as Robinson was shown a straight red card by referee Andy Woolmer for scything down Wilson.
Arter was denied a fifth Bournemouth goal when his blistering 20-yard strike clattered the bar.
Source: PA