The third goal of Nani's largely disappointing season and Javier Hernandez's 15th strike of the campaign saw the hosts through, although McAnuff's late effort ensured the Red Devils were never able to relax.
The win keeps United on track for a repeat of their historic 1999 treble, and Sir Alex Ferguson on course for a possible encounter with Rafael Benitez, whose Chelsea team must beat Middlesbrough for the right to face the Red Devils in the last eight.
A goalmouth scramble after just 90 seconds saw Hernandez's shot blocked, Danny Welbeck fluff the rebound and Antonio Valencia finally head straight at Adam Federici.
As it turned out, it was one of Federici's least taxing jobs. The Reading goalkeeper was also forced to deny Welbeck and Ashley Young had a shot blocked before the visitors got into their stride, with Noel Hunt to the fore.
Hunt sustained a nasty cut following a collision with Nemanja Vidic that required two shirt changes, but also set the pattern for a bruising collision between the pair.
Nani's introduction had undoubtedly been significant and moments after his effort had been repelled, he strode onto Valencia's cross and supplied a deadly finish. When Hernandez flashed home a near-post header on United's next attack, it appeared their work was complete.
Instead, McAnuff struck nine minutes from time to bring a familiar sense of nervousness to Old Trafford which only Andre Marriner's final whistle was able to ease.
Fa Cup highlights and behind the scenes shots from the game below