The Liga champions showed few signs of rustiness as they coasted to victory in their first friendly of the 2012-13 campaign, with Lucas Vazquez among those to impress
Lucas Vazquez opened the scoring for Los Blancos, who effectively killed the game off with a quick-fire double just before the break. Denis Tcheryshev doubled the Spanish champions' advantage before Esteban Granero added a third moments later.
Matar Diop did give the home fans something to cheer when he netted shortly after the interval but Di Maria, who was introduced during the break, extended Madrid's advantage yet further before putting the seal on a comfortable win for Madrid with a second goal in the closing stages.
Jose Mourinho's men did not look remotely rusty early on, with the impressive Vazquez putting the visitors a goal to the good after just nine minutes of play courtesy of a sublime right-footed finish, showing exquisite technique in controlling a diagonal ball in behind the Oviedo defence.
Russian attacker Tcheryshev strengthened Madrid's lead on 38 minutes after being put in on goal by Alvaro Morata and they soon went 3-0 up when the ball rather fortuitously clipped Granero on its way into the net after a game of pinball in the box following an incisive run from Vazquez.
Diop pulled a goal back for Oviedo early in the second half but Di Maria replied in kind moments later after capitalising on some desperately sloppy defending from the home side and the Argentine was on hand to net the rebound from Gonzalo Higuain's shot, which had come back off the post.
Madrid will now face Benfica on Friday before travelling to the United States to take on the LA Galaxy on August 2.