Louis van Gaal's side started the game strongly and duly took the lead through Rafael van der Vaart. The midfielder latched onto Van Persie's pass and fired an effort low and hard into the bottom corner.
Adrian Popa could have got the visitors back in the game but his shot was well saved by Kenneth Vermeer who got down well to his right, after the defender picked up Gabriel Tamas's headed pass.
After the break, the hosts looked to extend their lead but first Van Persie then Van der Vaart missed good opportunities when well placed in the penalty area.
Minutes later, Van Persie did get his side's second with a well-placed header which beat Costel Pantilimon, as he got on the end of Arjen Robben's pinpoint cross.
It was three shortly after, when Jeremain Lens was fouled in the penalty area by Florin Gardos and Van Persie notched his second of the game converting the spot kick into the bottom corner.