Fraser's close-range finish midway through the first half and Wilson's stoppage-time effort proved the difference as Eddie Howe's men ended a run of three opening weekend defeats.
Wilson, scorer of eight league goals last term, had an earlier chance to put the result beyond doubt before half-time, but his spot-kick was well saved by Neil Etheridge, the goalkeeper becoming the first player to save a penalty on his Premier League debut since Allan McGregor for Hull City in August 2013.
It was to prove the only real joy for last season's Championship runner-up, though, as a more competitive performance after half-time went unrewarded.
Cardiff's low-key off-season spending has prompted widespread predictions of an immediate return to the Championship and its deficiencies were evident across a one-sided first 45 minutes.
Dominant in possession, Bournemouth turned its superiority into a deserved opener in the 24th minute as Fraser timed his run well to sweep home Wilson's intelligent cut-back.
Wilson should have opened his own account just beyond the half-hour mark, but, having been felled in a tangle with Bruno Ecuele Manga, the striker failed to beat Philippines international Etheridge, who turned the low attempt around his left post.
The visitors were far livelier after the interval and, spared by David Brooks's poor header at one end, almost scrambled in an equaliser with 25 minutes remaining, only for Asmir Begovic to deny Sean Morrison on the line.
Bournemouth eventually reasserted a sense of stability and the second goal came in the 91st minute when Simon Francis bustled his way to the byline and found Wilson for a cool low finish into the bottom far corner.
Cardiff heads back to Wales for the visit of Newcastle United next weekend, while Bournemouth's first trip of the season sees it visit West Ham United.