Parry put Cardiff ahead in the seventh minute and added another in the 12th before League Two Bournemouth staged a brave rally.
Parry's first goal came from a pass by Peter Whittingham and he ran 30 yards through a big gap in the home defence before scoring with a low left-foot shot.
Bournemouth's defence was again suspect six minutes later when a bad back pass from Warren Cummings was intercepted by Parry, who headed the ball into an empty net.
Cardiff should have had more as they dominated the first half hour.
Stephen McPhail, Whittingham and Jay Bothroyd all went close before Bournemouth pulled a goal back with their first shot on target.
Glenn Loovens gave the ball away to Darren Anderton and little striker Jo Kuffour accelerated away from Roger Johnson before scoring with a left-foot shot.
Bothroyd contrived the miss of the match just before half-time when he somehow shot over from six yards after goalkeeper Shwan Jalal had parried a header from Johnson.
For all the divisional advantage, Cardiff were obliged to defend in the second half as Bournemouth pressed for an equaliser.
In injury time, Cardiff goalkeeper Tom Heaton had to go down to deny substitute Ricky Sappleton a goal on his debut after arriving on loan from Leicester.
On the break Cardiff might have increased their lead but Jalal denied Parry a hat-trick when he rushed out to block his shot and then, also in injury time, the goalkeeper did the same to stop substitute Miguel Comminges from adding a late third.
Bournemouth Official Website
Cardiff Official Website