Despite the boost of an early breakthrough, the Reds were unable to kill off the visitors in the first half. Van Persie netted at the second attempt, after David Marshall saved his initial effort superbly, when Antonio Valencia's header came back off the bar.
Debutant Juan Mata was close to finding Ashley Young with a deep cross and van Persie screwed agonisingly wide but the Welsh side had clear-cut chances of their own. Craig Noone fired over after a promising run and David De Gea had to keep out a Mark Hudson header with an outstretched boot.
Cardiff also enjoyed a decent spell of possession after the interval but Young doubled the lead with a moment of individual brilliance, drifting inside onto his right foot and burying an unerring low drive into the bottom corner of Marshall's net.
It sparked more attacking play from David Moyes' men with Mata's first shot in a red shirt saved by Marshall and Jonny Evans bending wide after galloping forward with purpose. Wayne Rooney came on for van Persie and went close with a deflected drive.
Marshall parried a Valencia drive onto the woodwork after the Ecuadorian delayed his shot and turned Declan John before Mata, his replacement Adnan Januzaj and Rooney all had decent efforts. However, the visitors were competitive until the final whistle on a night when respect was paid to their manager.