Second-half goals from Nani and Chicharito were enough for the hosts to claim the win, despite a late goal from Jobi McAnuff, as they march on to face either Chelsea or Middlesbrough.
Both sides made wholesale changes to their teams with just David de Gea, Phil Jones and Danny Welbeck keeping their places in the side for the hosts, while Reading handed Adam Le Fondre a rare start.
Sir Alex Ferguson's men got off to a flying start and might have opened the scoring in the opening minutes. Almost straight from the kick-off Chicharito saw a low shot blocked, but neither Welbeck nor Antonio Valencia were able to slot the loose ball home.
Less than a minute later, Welbeck again went close. Some clever work by Ashley Young saw him slip the ball through to the striker but his low shot was saved by Adam Federici.
Yet Reading slowly came back into the game, pressing United high up the pitch and looking a real threat at set pieces.
Indeed United had the returning Nemanja Vidic to thank on 17 minutes, as the centre-back did superbly to head Nicky Shorey’s free-kick to safety with Sean Morrison poised to head home.
As the first half drew to a close United were forced into a change, with Phil Jones hobbling off after a strong challenge by Jobi McAnuff.
Substitute Nani made an instant impact on the game, smashing a right-footed volley across goal and onto the post before forcing Federici into another good stop with a stinging left-footed shot as the hosts ended the half strongly.
The Red Devils emerged after the interval with a greater tempo but struggled to convert their greater urgency into clear-cut chances, leading to the arrival of Robin van Persie for Young just after the hour mark.
The Dutchman’s arrival helped United take almost complete control of the game, forcing Reading further and further back until finally the Royals’ resistence was broken.
With 69 minutes on the clock, Valencia carried the ball down the right before passing to Nani in the box, who took one touch before poking past Federici to break the deadlock.
Minutes later the game appeared effectively over as a contest, as United grabbed a second. Again the danger came down the right, this time through goalscorer Nani who crossed for Chicharito to nod home at the near post and double United’s lead.
Yet with 10 minutes to go a lapse in concentration in the United defence set up a nervous finale after McAnuff pounced on some awful defending to drive past De Gea from close range.
Reading have made late comebacks their speciality at times this season, but on this occasion there was to be no fairytale, as United held on to continue to fight on three fronts while the visitors must concentrate on their fight for Premier League survival.