Marc McNulty gave the visitors the lead in the 36th minute at Loftus Road after they dominated the early stages of the game. Louis Reed played McNulty in, and he slotted home past Alex McCarthy.
Rangers struggled throughout with Matt Phillips, Bobby Zamora and Leroy Fer all missing chances.
QPR became the latest cup scalp for the League One side after wins over Aston Villa, Fulham, West Ham and Southampton in recent seasons.
Campbell-Ryce netted early in the second half after keeper Alex McCarthy was unable to claim Reed’s corner and he struck again in the final seconds when he gratefully collected 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 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 it was still an experienced side which included 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 from the start.
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 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 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.