Despite the result Argyle had plenty of chances either side of the half and the game could have quite easily have ended five all, but United defended well to record their tenth victory out of eleven games.
The Blades came out at the Pilgrims from the start but it was the visitors who were handed the first scoring opportunity. Five minutes in Bjarni Gudjonnsson floated the ball into the box which fell to Nick Chadwick but the ex-Everton striker failed to control the ball as the chance went begging.
However five minutes later Tont Pulis men suffered the same fate as Derby County last Saturday, conceding an early goal. A fine move in defence put David Unsworth free on the left hand side, he switched play and delivered a powerful cross over to Paul Ifill from the half-way line.
Ifill, a menace as ever crossed for NEIL SHIPPERLEY who headed towards goal, Argyle keeper Romain Larrieu stopped the shot but the ball somehow bounced back into the net as Shipperley watched the ball trickle over for his fourth of the season.
The visitors then went close on 19 m inutes, Paul Wotton produced a speculative effort from all of 25 yards, the ball bobbled and bounced before slamming against the post past a worried Paddy Kenny.
Steven Kabba went close to adding a second for United, Shipperley cut Kabba through on goal who turned before seeing his shot whistle past the post and into the kop.
But on 30 minutes gone on the clock the home side doubled their lead. Quinn was tripped by Anthony Barness as he headed towards goal, referee Graham Laws chose to book the former Bolton defender rather than produce the red card. However the free-kick paid off, as Quinn, Unsworth and Ifill all looked to be taking it ALAN QUINN moved quickly to fire home.
Argyle then hit back, Nick Chadwick got goalside of his marker to shoot from six yards, Kenny (who was marking his 300th professional appearance) got down quick to deny a shot that looked goal bound.
HALF-TIME: SHEFFIELD UNITED 2-0 PLYMOUTH ARGYLE
The vistors came all out at United in the second half and forced Kenny into two close shaves on 54th minute, Chadwick shot on goal for the former Bury keeper to push away while Nick Montgomery cleared off the line at the far post after Micky Evans headed towards goal.
On 57th minute Pulis made a triple substitution. Djordjic, Buzsaky and Taylor coming on to replace Brevett, Gudjonsson and Chadwick.
Alan Quinn then created a chance for the Blades, he released Steven Kabba who was denied twice by Larrieu and when the ball fell to Shipperley the former Palace striker saw his shot cleared off the line by Hasney Aljofree.
On 64th minute Shipperley made way for Vincent Pericard in an entertaining half, Kabba shot wide after a neat one-two with Montgomery but this was after Bjordjic's through ball released Scott Taylor who shot low which Kenny saved.
Argyle's third substitute Akos Buzsaky tested Kenny from 35 yards as the visitors got on top of the game. With 13 minutes left Leigh Bromby nailed the ball over his own cross bar when Taylor attempted to close down Evans' chip into the box.
The Blades came close to making it 3-0 when Alan Quinn once again took opportunity of a free-kick which was tipped onto the crossbar by the Pilgrims keeper before Larrieu again denied Quinn at close range near the end.
FULL-TIME: SHEFFIELD UNITED 2-0 PLYMOUTH ARGYLE
Man of the Match: Alan Quinn