First-half goals from Juan Mata and Romelu Lukaku sealed United's progress against their Championship opponents as they continued their 100% record under interim boss Ole Gunnar Solskjaer with a fifth win from five.
However, Reading can take a lot of encouragement from their performance, having ended the match with more shots and more possession than the 12-time FA Cup champions.
Both the form book and the league tables suggested a comfortable home win, but it was Reading - 23rd in the Championship and now without a win in 11 - who settled quicker than a United side containing the likes of Alexis Sanchez and Lukaku.
The hosts did burst into life in the 16th minute when Lukaku, Fred and Scott McTominay were all involved in a slick move to set up Sanchez, who fired an effort narrowly over from just outside the area.
Reading hit back immediately, though, and created their first chance of the contest less than a minute later when Garath McCleary's pass went all the way through to Andy Yiadom, who sliced his finish well off target when he should have done better.
Fred had the ball in the back of the net shortly afterwards and, while the goal was correctly disallowed for offside, a lengthy VAR consultation lasting more than two minutes ruled that there had been a foul on Mata before the ball squirmed its way through to the Brazilian midfielder.
Referee Stuart Attwell therefore pointed to the spot, and Mata tucked the penalty away himself to settle any United nerves following an unconvincing start.
Lukaku almost doubled that advantage when he was played through on goal by Fred, but he got the ball caught underneath his feet and his eventual shot was too close to Anssi Jaakkola.
Once again, Reading responded in kind and their best chance of the first half went begging on the half-hour mark when Callum Harriott sent Danny Loader through on goal, only for the striker to take too long over his finish as he tried to take the ball around Sergio Romero.
The Royals were more than holding their own against their illustrious hosts, though, and Harriott squandered two long-range opportunities before Yiadom stung the palms of Romero at the near post with a powerful strike on the turn.
However, just when it looked as though the visitors might equalise, United doubled their advantage with the last major action of the first half as Lukaku latched on to Sanchez's incisive pass before rounding the keeper and sliding his finish into an empty net for his third goal in as many games.
It made for a harsh half-time deficit as far as Reading were concerned, but the Championship outfit did not let their heads drop as Jon Swift flashed a couple of long-range efforts towards goal before Harriott fired a golden chance too close to Romero from inside the area.
Solskjaer felt confident enough with his side's two-goal lead to hand a first-team debut to highly-rated youngster Tahith Chong, although moments later he was struck with a blow as Sanchez - only just back from a hamstring injury - limped off with what looked like a recurrence of the problem.
Marouane Fellaini - also on as a sub - was the next to come close when he failed to generate enough power to steer a close-range effort past the keeper after good work from Ashley Young, but the plucky visitors were soon on the front foot once again.
This time Young was at fault having been caught in possession inside his own half, and the move ended with Sone Aluko's scuffed strike forcing a full-stretch save from Romero to turn it behind for a corner.
United saw out the match in a professional manner during the closing stages, though, and almost added a third with the final meaningful action of the game when Andreas Pereira was denied by a fine stop from Jaakkola.
The result leaves Reading boss Jose Gomes still searching for his first win in charge of the Royals - who as a club have not won a game since November 3 - but the visitors will take encouragement from their performance despite once again failing to score in another defeat.
MAN UTD (4-3-3): Romero; Dalot, Darmian, Jones, Young; McTominay, Pereira, Fred (Fellaini 62'); Mata (Chong 62'), Lukaku, Sanchez (Rashford 64')
READING (4-2-3-1): Jaakola; Yiadom, Ilori (Aluko 46'), Moore, Richards; Kelly, Rinomhota; McCleary (Barrow 61'), Swift, Harriott (Meite 76'); Loader