Royals avoided the kind of fourth-round slip up suffered by Spurs, Liverpool, QPR, Norwich City and Aston Villa - who all crashed out to lower league opposition - with an impressive victory and their fifth win in six games.
There was no such scare as the Madejski Stadium with Reading's superior quality proving too much for the valiant Blades.
Hunt's opportunities have been limited of late, but he gave McDermott a timely reminder with an important brace.
The Irishman, who is currently negotiating a new contract, notched his first on five minutes by heading home a Hal Robson-Kanu cross.
And he grabbed his second on 50 minutes after converting a Garath McCleary centre.
Mikele Leigertwood had put Reading 2-0 up six minutes before the break with a long-range bullet and McCleary netted the fourth with a smart run and finish 54 minutes in.
Meanwhile, there was a fitting tribute to Chris Amrstrong in the third minute observed by all supporters at the game.
The full-back wore the No.3 shirt for both clubs before multiple sclerosis forced him to retire in 2011.
Reading's reward is a juicy trip to Manchester United in the FA Cup fifth round on the weekend of February 15/16.
Royals: Federici; Kelly, Shorey, Mariappa, Morrison; Karacan, Leigertwood (c) (Guthrie 84), McCleary, Robson-Kanu; Hunt, Le Fondre. Subs not used: Taylor, Cummings, Pearce, Guthrie, Kebe, McAnuff, Church.
Blades: Long; McMahon, Westlake (Collins 76), Higginbotham, Maguire; Doyle (c), McDonald (Whitehouse 70), Murphy, Blackman, Porter (Flynn 60), Kitson. Subs not used: Coyne, Collins, Ironside, Flynn, Whitehouse, Cresswell, De Girolamo.