Following Monday's 4-1 home defeat by Watford, another two points dropped against mid-table Plymouth leaves the second-placed Blades 13 points adrift of runaway leaders Reading, with Watford gaining further ground.
The silver lining was a much-needed clean-sheet from a hard-fought game in which no quarter was asked, and none given.
The best chance of the game came in the very last minute when Argyle midfielder David Norris was teed up by Tony Capaldi, but his powerful shot was saved by United goalkeeper Paddy Kenny.
The visitors' most threatening moment also came towards the end when Argyle goalkeeper Romain Larrieu's hashed kick hit his own defender Mathias Kouo-Doumbe's back and presented Ade Akinbiyi with a clear run-in on goal.
Kouo-Doumbe's swift tracking back drove Akinbyi wide, though, and he was unable to direct anything on target.
Argyle handed a debut to on-loan Portsmouth forward Vincent Péricard as a second-half substitute, and the former Juventus man could have scored with his first kick when well placed but volleyed high over the crossbar.
That was one of a few scares for Sheffield United's defence, that showed two changes from the one breached four times by Watford - with re-called captain Chris Morgan a particularly steadying influence.
United, who gave a full debut to Garry Flitcroft in place of Michael Tonge, started brightly but created only one half-chance when Morgan's overhead free-kick slightly extended Larrieu.
Argyle's response was a right-wing Anthony Barness cross that Michael Evans flick-headed on for Nick Chadwick to send a powerful header past Kenny but wide of the goalpost.