With the Royals sitting just inside the Premier League relegation zone, many had marked this fixture as a potential upset, but the hosts' clinical finishing ensured they romped to victory against the League One visitors.
Noel Hunt gave Reading a fifth-minute lead, but United came into the game in the following half-hour only to see Mikele Leigertwood give the home side a two-goal cushion with a fine 25-yard drive against his former club.
Hunt's second, and a second-half strike from Garath McCleary, put the result beyond doubt in the second half.
With rivals Norwich and QPR both being knocked out by lower-league opposition yesterday, McDermott was happy his side got themselves in the hat for the last 16 – even though the scoreline was, perhaps, a little harsh on the Blades. "If you look at the results today, a couple of big teams have gone out and we are thankful we are not one of them," the Reading manager said.
"I don't think we did particularly well in the first half. We just weren't ourselves. I got a bit agitated, which is unusual for me.
"But we were much more clinical and efficient after, so we deserved to go through."
Having looked like certainties for relegation towards the end of 2012, Reading now find themselves welcoming Chelsea to the Madejski Stadium on Wednesday on the back of a four-match winning streak.
The high morale in the camp bodes well for the Berkshire club's chances of avoiding the drop and also boosts their hopes of maintaining their strong history in the FA Cup, where they have reached the quarter-finals in two of the past three years.