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 them looking largely disjointed.
Reading, who sit 23rd in the 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 following a VAR consultation, with Fred's strike having been disallowed for offside in the same move.
It was harsh on Reading, who had started better, and they 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 injury 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 were mostly comfortable in the closing minutes as they secured their place in next Monday's fourth-round draw.
What does it mean? Solskjaer streak continues but Sanchez a worry
A fifth victory from his first five games in charge will do no harm to Solskjaer's chances of getting the job permanently, even if this was not a particularly strong performance from his much-changed side.
However, while their hopes of a third FA Cup final in four seasons remain intact, the sight of Sanchez asking to come off in the second half of his first start since early November will not be a welcome sight.
The Chilean did sit on the bench after going off, so Solskjaer will hope the forward was merely being cautious ahead of a training camp in Dubai.
Scott McTominay was one of United's only consistently good players throughout the match, winning seven tackles and ending the game with the best pass completion rate of any of the home side's starting XI (92.3 per cent).
Pereira out of sorts
Andreas Pereira was caught in possession one too many times in the first half, once on the edge of his own penalty area. He does not look all that comfortable in a deep midfield role, even if Solskjaer and Jose Mourinho have used him there.
Key Opta Facts
21 - Juan Mata has been directly involved in 21 goals in 24 starts in the FA Cup (10 goals, 11 assists). Specialist. pic.twitter.com/WB1kgGwrdv— OptaJoe (@OptaJoe) January 5, 2019
- United have lost just one of their last 52 FA Cup games against teams from a lower division (W44 D7), suffering defeat to Leeds United in January 2010.
- Sanchez has been directly involved in 18 goals in 19 FA Cup games (nine goals, nine assists).
- Lukaku has scored 13 goals in his last 14 FA Cup appearances, including six in seven for the Red Devils.