Goals from Graham Coughlan, Paul Wotton and substitute Dexter Blackstock gave the Pilgrims the points against a United side forced to replace injured goalkeeper Paddy Kenny with outfield player Phil Jagielka midway through the first half.
Despite their recent morale-sapping run - which has plunged Bobby Williamson's side towards the brink of the relegation zone - Plymouth wasted little time in attempting to rectify matters against the Blades.
They tore into Neil Warnock's side from the outset and showed little sign of the failings which saw them capitulate 5-0 at West Ham on Saturday.
By contrast, United struggled to match their heroics of three days earlier when they battled to a 1-1 FA Cup fifth-round draw against Arsenal at Highbury.
Barely a minute had passed before midfielder Akos Buzsaky whipped in a dangerous cross which Leigh Bromby was forced to clear - but the hosts soon drew first blood.
Northern Ireland winger Tony Capaldi collected the ball on the left flank before delivering a delightful ball into the box, where Coughlan volleyed into the bottom left-hand corner for his second goal of the season.
Suitably inspired, Plymouth continued to press - and Wotton's 25-yard free-kick went just the wrong side of the right post.
The visitors began to gain a foothold on the game, and Andy Liddell's shot from distance went inches wide before Michael Tonge was booked for dissent.
Despite his indiscretion, Tonge began to emerge as a key figure for the Blades -and his intricate efforts in midfield proved a constant source of unease for the hosts.
Liddell's dangerous cross was cleared by Hasney Aljofree before another teasing delivery by Liddell was fired just wide from six yards out by Tonge.
The Blades were dealt a massive blow after 28 minutes when Kenny was forced off through injury - and with no recognised goalkeeper on the bench, Warnock replaced the shot-stopper with Jagielka.
While the United utility player was largely unemployed during the remainder of the first period, he was well and truly beaten two minutes after the restart.
Wotton collected the ball 25 yards out and drilled a fierce right-footed effort into the bottom left-hand corner to hand his side a 2-0 advantage.
United almost hit back immediately, but Jon Harley's 25-yard effort was bravely blocked by David Norris.
With Capaldi an increasingly influential figure in midfield for Plymouth, the hosts began to dominate possession and looked more likely to add to their two-goal advantage than allow United the lifeline of a goal.
Nick Chadwick fired narrowly wide, before Micky Evans headed just off target from six yards.
In a tactical switch, Warnock replaced Tonge and Paul Shaw with Jonathan Forte and Alan Quinn - but they struggled to make an impact as Plymouth remained on top.
Blackstock, on as a second-half replacement for Evans, nodded home Peter Gilbert's left-wing cross to complete the victory for Plymouth.