Mata came close with an effort of his own after eight minutes, but the Spaniard fired a Ander Herrera cross over the crossbar from just outside the box.
United were ahead after 24 minutes, however, when Angel di Maria floated a free kick into the back of the net, with the away side's defence only able to watch his effort drift into the top corner.
QPR's main threat came from high balls into Charlie Austin, but the striker had little support each time he won a flick-on. At the other end, Van Persie had another half-chance for United after 31 minutes, but his header was over the crossbar.
United had their second after 36 minutes when Herrera shot into the bottom corner following a blocked effort from Rooney, who got in on the act late in the half with an arrowed effort past Rob Green.
United boss Louis van Gaal has handed debuts to Rojo and Daley Blind, while Di Maria is making his home debut for the Premier League outfit. Colombian hitman Radamel Falcao is waiting in the wings on the bench.