The mercurial Portuguese winger was sent on just before half-time in place of the injured Phil Jones and he scored United's opener before setting up Javier Hernandez for the second.
Reading pulled one back through Jobi McAnuff but United held on to set up a quarter-final against second-tier Middlesbrough or European champions Chelsea.
The Premier League leaders dominated the match but struggled to make the breakthrough in the face of resolute Reading defending and a fine performance by goalkeeper Adam Federici.
"It was a really good cup tie, when they got the goal they went for it and piled men in the box," Ferguson told ESPN.
"We played some great football and could have scored a lot of goals tonight.
"I'm satisfied with the quality of our play. We should have punished them better though. At 2-0 you are never comfortable.
"Nani deserved to be man of the match, his contribution was terrific. I had a feeling he would win the match for us."
Nani, linked with a move away from Old Trafford, struck the post with a fierce angled volley shortly after coming on and he injected energy into a much-changed United side from the 1-1 Champions League draw at Real Madrid last week.
Robin van Persie, Michael Carrick and Rio Ferdinand started on the bench and Wayne Rooney was left out of the squad after suffering a bout of sinusitis.
United won 4-3 at Reading in a dramatic Premier League match this season and they started brightly by creating several chances to open the scoring.
But Federici made a succession of good saves and the visitors slowly established a foothold in the match.
Nani grabbed the first goal with a cute volley from 12 metres after 69 minutes and his pinpoint cross set up Hernandez for a trademark near-post header soon afterwards.
Reading refused to lie down and McAnuff scored nine minutes from time with a neat finish from close range.
The side third from bottom of the Premier League table continued to press forward but the hosts, bolstered by the reassuring presence of experienced Serbian Nemanja Vidic at the heart of their defence, hung on.
United, record 11-times FA Cup winners but who have not lifted the trophy since 2004, remained on course to repeat their treble of 1999, 12 points clear of Manchester City in the Premier League and level at 1-1 with Real Madrid after the Champions League last 16 first leg match.
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