Marc McNulty slotted in a 36th-minute opener for the League One side after being put through by Louis Reed’s pass, and Campbell-Ryce netted early in the second half after keeper Alex McCarthy was unable to claim Reed’s corner.
Campbell-Ryce struck again in the final seconds when he gratefully collected Leroy Fer’s wayward back-header and skipped past McCarthy to cap a brilliant Blades victory.
The result continued United’s remarkable recent cup record. Nigel Clough’s men reached the FA Cup semi-finals last season, beating top-flight Aston Villa and Fulham along the way, and have knocked Southampton and West Ham out of the this term’s Capital One Cup.
QPR, meanwhile, have suffered numerous early exits, several against lower-division opposition, in the 18 years since they last made it past the FA Cup third round without needing a replay. The west London outfit have won only two cup ties in the last 11 years.
Rangers boss Harry Redknapp made seven changes to his starting line-up but nevertheless named an experienced side which included the likes of Rio Ferdinand, Fer and top scorer Charlie Austin.
They made a decent start, with Fer seeing a stinging shot saved at the near post by keeper Mark Howard, who also kept out an effort from Jordon Mutch.
But the R’s never looked comfortable at the back and Campbell-Ryce gave the hapless Armand Traore the runaround on the right flank.
Stefan Scougall was also a constant threat for the visitors and fired over before they eventually went ahead nine minutes before half-time courtesy of McNulty’s ninth goal of the season.
Redknapp sent Bobby Zamora on at half-time in an effort to change the course of the game, but United were two ahead within four minutes of the restart.
Traore needlessly conceded the corner, and McCarthy, in for the rested Rob Green, got nowhere near Reed’s right-wing delivery. After the ball bounced off Mutch, Campbell-Ryce had the simple task of scoring from close range.
Zamora squandered a golden opportunity to quickly pull a goal back when he headed Matt Phillips’ cross wide of the target.
Phillips was also guilty of a glaring miss, slicing a shot high and wide from inside the box following a surging run by Mauricio Isla.
Rangers, whose electrifying performances at Loftus Road have given them a fighting chance of avoiding relegation, were listless throughout.
Fer’s stoppage-time error in the build-up to the third goal summed up their display and they were booed off by the home fans at the final whistle.