First-half goals from Juan Mata and Romelu Lukaku were enough for the home side at Old Trafford, although the nine changes made to the team that won at Newcastle United left it looking largely disjointed.
Reading, which sits 23rd in the EFL Championship, enjoyed 60 per cent of the possession and had 13 shots to United's eight, although a comeback never truly looked likely.
The downside was the fact Alexis Sanchez had to go off 64 minutes in, having apparently hurt the hamstring that kept him sidelined throughout December.
Mata dispatched a cool penalty — his first FA Cup goal since the victorious final of May 2016 — after referee Stuart Atwell penalised Omar Richards for a foul on the Spaniard after a VAR (video assistant referee) consultation, with a Fred's strike having been disallowed for offside in the same move.
It was harsh on Reading, which had started better, and it should have been level when Danny Loader made a mess of a one-on-one with Sergio Romero after Lukaku was denied by Anssi Jaakkola at the other end.
Andy Yiadom was denied by Romero at his near post as United continued to struggle, but a stray pass from John Swift proved costly in first-half stoppage-time, with Lukaku rounding Jaakkola to make it 2-0 from Sanchez's throughball.
Solskjaer handed youngster Tahith Chong the chance to impress off the bench and was then forced to take off Sanchez, who indicated his troublesome right hamstring was again causing him discomfort.
Sone Aluko was denied by a good save from Romero, but United was mostly comfortable in the closing minutes as it secured their place in the fourth-round draw.