United yet again fielded a strong eleven for this afternoon's clash, something they did in the previous round against Bristol Rovers.
Their triumph over the Rovers gave the Blades that winning feeling for the first time since July 2020 as Chris Wilder's men kick-started their season, following up their cup win with an impressive win over Newcastle United. Their first of the league campaign.
Wilder will be hoping this afternoons victory gives the Blades some much needed confidence ahead of their upcoming trips to both Manchester Club's.
The story of the match
Sheffield United dominated the first half of the tie, there would be no prizes for guessing which side was playing in England's top flight.
The Blades had most of their fun down the left hand side through Edna Stevens. He found his team mates on numerous occasions in the box but much like the story of United's season so far, they were unable to convert chances into goals.
Plymouth spent most of the first half-hour restricted to defending their own 18-yard box as the Blades tried to find a combination that would unlock Argyle's defence.
Jayden Bogle had the first big chance of the afternoon as Stevens' cross found the full back unmarked at the back post, although he was unable to trouble Cooper as it trickled out for a goal kick.
Plymouth nearly caught the home side out just before the half-hour mark, when a rare attack from the League One side allowed Luke Jephcott to tee up Panutche Camará, who fluffed his lines at the vital moment, as he sent his effort into the Bramall Lane Kop.
Missing a chance as big as the one Camará did was always going to come back and haunt Ryan Lowe's side, and it wasn't long before Chris Basham did exactly that.
With five minuets left of the first half Wilder's side but together a fantastic passing move - reminiscent of the football we saw from the Blades last season - before Billy Sharp's cross was perfectly weighted for Sheffield United's Mr Reliable, Chris Basham, to head home.
The goal eased any fears in the home dugout of a potential FA Cup upset.
The second half was always going to be an easier exercise for the home side as Plymouth had forty-five minuets to keep their cup dreams alive.
Blades captain, Sharp, firmly put the dagger in the Argyle hearts ninety seconds after the restart. Oliver Norwood split both opposition centre halves with his pass from deep, before Sharp rounded the helpless Cooper, as he slotted home into an empty net to double the home sides advantage.
The game seemed to be heading for a rather routine finish, with Sheffield United looking at it as a case of how many goals they were going to finish the afternoon with.
That all changed with fifteen minuets left on the clock when Lowe's side found their way past United's leaky defence - like so many have before them this season.
United's inability to clear a rather routine phase of play came back to haunt them, something that seems to be a recurring theme at the the Lane this season.
Bryan Moore won the back high in the Sheffield United half before he slid the ball across the box to the on-coming Camará, who made no mistake with his effort from 6 yards out, presenting the Pilgrims with a lifeline.
The final stages of the game saw Plymouth camped in the United half as they looked to sneak in an equaliser.
Rhian Brewster and Sharp both made way for David McGoldrick and Oliver Burke as Wilder opted for fresh legs for the final proceedings in the hope of sealing the game off by catching the League One side on the break.
Sheffield United will now face Bristol City in the fifth round, after they beat Milwall 3-0 this afternoon.
Sheffield United: Ramsdale; Basham, Egan, Ampadu; Bogle, Lundstram, Norwood, Fleck, Stevens; Brewster, Sharp.
Plymouth Argyle: Cooper; Edwards, Aimson, Opoku, Watts, Grant, Camara, Fornah, Mayor, Hardie, Jephcott.