Vale started brightly with new signing Christopher Herd supplying a useful cross from the right that Luke Rodgers attempted to direct towards goal, but his shot flew high over the crossbar.
The visitors went ahead at the first time of asking when after ten minutes, Jo Kuffor's impressive run allowed him to shoot and, despite Joe Anyon's save, Sam Vokes followed up with a tap-in.
Bournemouth went close to doubling their lead seven minutes later when the Vale defence invited Danny Hollands to shoot and they almost paid the price with the ball striking Anyon's right post.
Hollands got it right second time around when Vokes' flick-on fell to the midfielder 12 yards from goal for him to control and volley into the bottom left corner of the goalkeeper's net.
The Valiants made an ideal start to the second half when Tobias Mikaelsson laid the ball off for George Pilkington, who sent a 20-yard left-footed strike past a helpless Ryan Price and into the back of the net.
Paul Edwards should have put Vale back on level terms in the 70th minute when Rodgers provided the perfect pass across the face of goal, but the substitute somehow failed to find the net, scuffing his shot.
Lee Sinnott's men were lucky not to go further behind in the 77th minute when an error by Adam Eckersley allowed Marvyn Bradbury a one-on-one opportunity, but Anyon stood firm to come out on top.
Any chance of a comeback was ended six minutes before the final whistle when Shaun Cooper converted his 20-yard free-kick, curling it expertly into Anyon's top left corner.