However, the real United hero was goalkeeper Paddy Kenny, who made several world-class saves as Argyle chased the game.
When Kenny was not the vital last line of defence, his back four came to his aid with several goal-line clearances.
In truth Argyle never featured in the game until they were a goal behind as they sunk to a first home defeat in four matches.
Argyle manager Paul Sturrock, a former Sheffield Wednesday manager, had stuck to the same starting line-up for the fourth successive match, but they were a shadow of the team that had won five of their last six games.
Driving rain and a swirling wind did not help either side and it was not until late in the first half that Argyle fashioned the first real goalscoring chance when Peter Halmosi's shot was cleared by Gary Naysmith with Kenny beaten.
Then Gary Teale found Halmosi at the far post and this time the Hungarian's on-target shot was thumped to safety by Blades captain Chris Morgan.
The best Argyle chance came after the interval when Lilian Nalis released Jermaine Easter, but the Pilgrims striker was denied by Kenny.
Almost immediately, United scored when Gary Speed set up a quick breakaway attack. The ball was worked to David Cotterill, who crossed for Beattie to head home unmarked from a couple of yards.
Kenny then saved a shot by Russell Anderson that hit Nadjim Abdou and looked destined to be the equaliser and then Matthew Kilgallon completed a hat-trick of goal-line clearances from Halmosi, after substitute Jamie Mackie had set him up.
Kenny saved his best until last as Argyle poured forward in injury-time, thwarting Mackie from close range