Casemiro netted a brace for the 20-time English champions, while Fred was also on the scoresheet, with Erik ten Hag's side proving to be too strong for their opponents on Saturday night.
Reading, who netted a late consolation, finished the game with 10 men, as experienced forward Andy Carroll was sent off in the 65th minute when he picked up the second of two bookings in the space of five minutes.
Man United, who last lifted the FA Cup in 2016, are still competing on four fronts this season, with the team also chasing success in the Premier League, EFL Cup and Europa League.
Reading had a chance to test Man United goalkeeper David de Gea inside the opening four minutes at Old Trafford, but Tom Ince's free kick from a brilliant position hit the home side's wall.
The Red Devils then had a half-chance down the other end, with Wout Weghorst's flick from an Aaron Wan-Bissaka cross deflected behind for a corner.
Christian Eriksen was next to come close, striking a free kick just wide of the Reading post in the eighth minute; the Denmark international had another opportunity in the 14th minute, with his goal-bound strike being blocked after Marcus Rashford's free kick was parried by Joe Lumley.
Antony then bent one just wide of Lumley's goal in the 17th minute, before Weghorst had a shot, which looked to be heading in, blocked behind for a corner, with Man United very much on the front foot on home soil.
Tom Holmes was impressing at the heart of the Reading defence, with the 22-year-old throwing his body in the way of a number of shots, as the pressure increased from Ten Hag's side, and Bruno Fernandes only just missed the post with a placed effort in the 27th minute.
Fernandes had another chance in the 32nd minute after excellent work from Antony down the right, with the Portugal international firing just wide of the far post.
Man United thought that they had made the breakthrough in the 35th minute through Rashford; Weghorst headed into a dangerous area, and Rashford was on hand to nod home at the far post, with Lumley unable to prevent the ball from crossing the line, but a VAR check showed that Weghorst was offside in the build-up.
The home side had a shout for a penalty in the 40th minute when Casemiro went down inside the box under a challenge from Junior Hoilett, but the referee was not interested and VAR agreed.
Antony missed the target with another curler in the period that followed, with the Brazil international causing the Championship side problems with his movement.
Reading then had a golden chance to make the breakthrough just before the interval through Hoilett after a mistake from Tyrell Malacia, but De Gea was on hand to make a smart save.
The final opportunity of the first half fell to Man United, with Casemiro finding Weghorst inside the box, but the striker's effort was deflected into the arms of the Reading goalkeeper.
Fernandes struck high of Reading's goal early in the second half, with Ten Hag's side picking up where they left off, and the breakthrough finally arrived in the 54th minute through Casemiro.
The pass was from Antony, with the attacker expertly finding the run of Casemiro, and the midfielder brilliantly lifted the ball over the onrushing goalkeeper to make it 1-0 to the Red Devils.
Casemiro then doubled Man United's advantage just before the hour, as the summer arrival from Real Madrid picked out the bottom corner with a long-range strike, albeit with the help of a deflection off Holmes.
Reading were reduced to 10 men in the 65th minute of the match when Carroll slid into Casemiro, with the experienced striker picking up his second yellow of the match.
Man United scored a third less than a minute later, with Fred expertly flicking a Fernandes cross into the back of the net through the legs of the Reading goalkeeper.
The home side had another golden chance 20 minutes from time, but Alejandro Garnacho saw his low strike kept out by Lumley, and Weghorst could not bundle the ball home at the far post.
Reading had a lifeline in the 72nd minute when Amadou Salif Mbengue headed home from a corner, with the away supporters having something to cheer at Old Trafford.
Man United were quickly back on the front foot, though, with Garnacho and Facundo Pellistri both bright in the wide areas, having entered the field as substitutes alongside Kobbie Mainoo and Anthony Elanga.
Garnacho fired into the body of substitute Reading goalkeeper Dean Bouzanis 10 minutes from time, before the talented youngster set up Antony, who miskicked the ball in front of goal, with the home side ultimately declaring at three.
Man United will now switch their attention back to the EFL Cup, with the Red Devils boasting a 3-0 lead over Nottingham Forest heading into the second leg of their semi-final on Wednesday.
Reading, meanwhile, will be back in Championship action at home to Watford next weekend, with the Royals looking for their first league victory since the end of December.