Rosa and Miller struck in each half to fire Wolves into sixth place – for the first time since New Year's Day – replacing Preston who could only draw at Brighton.
Jones could have no complaints with Cardiff's first defeat in four away games as Wolves thoroughly deserved their fourth win in the last six matches.
Apart from a spell in the final 20 minutes of the first half, Wolves were dominant with Rosa's first goal for the club after his January arrival from Ferencvaros and Miller's second-half penalty sealing their success.
The only downside to the game was that the start of the second half was delayed by 15 minutes following crowd problems involving the Cardiff fans in the Steve Bull stand.
Wolves controlled the opening exchanges and it was no surprise when Rosa gave them the lead.
Paul Ince tested Cardiff's goalkeeper Neil Alexander from long range before Jeremie Aliadiere fired wide.
Aliadiere then turned provider with a low left-wing cross that was turned home at the far post by Hungarian international midfielder Rosa in the 15th minute to give Wolves a deserved lead.
Cardiff would have slipped further behind five minutes later only for Aliadiere to be denied by a smart save from Alexander.
That let-off sparked Cardiff into life with the impressive Jason Koumas driving City on.
Koumas, who was lucky not to be sent off for his 22nd minute lunge on Rosa, and Neal Ardley both went close before Steven Thompson fired his header straight at Stefan Postma.
Postma did his best to gift Cardiff an equaliser on the stroke of half-time as he spilled a shot from Jeff Whitley but just about grabbed it back before the ball rolled over the line.
The delay in starting the second half took the wind out of Cardiff's sails and Wolves effectively clinched their win eight minutes after the re-start through Miller's spot-kick.
Poland striker Tomasz Frankowski was sent tumbling to the floor by a push in the back from Neil Cox and Miller sent Alexander the wrong way from the resulting penalty.