A Chris Morgan own goal was enough to seal a narrow victory for Chris Hughton's side, while troubles mount for the under pressure Blades manager whose team are in freefall after carving out chances and squandering the lot.
The Sheffield side, seeking their first win in seven games should have snatched the lead after just three minutes, Ched Evans threading the ball into the path of Darius Henderson, but the big striker lashed his left foot strike across the face of the goal.
Newcastle response was immediate, Andy Carroll closing in from the left to drill in two close-range strikes, both blocked by full-back Kyle Walker.
Hughton's side escaped as United squandered another opportunity. Henderson unselfishly picked out Keith Treacy but from ten yards the on-loan Blackburn winger lashed the ball high over the bar.
The game turned scrappy with both sides guilty of passes going astray but United had the edge and almost went ahead seconds before the break, Evans running onto keeper Ian Bennett's long kick downfield, beating defender Fabricio Coloccini only to pull his low strike wide of the far post.
Newcastle, lethargic in the opening half, stepped up a gear, midfielder Ryan Taylor's curling shot towards the top right hand corner palmed away by Bennett before they went ahead in the 53rd minute.
Walker was caught in possession by Kevin Nolan, Taylor was the first to react, his low strike taking a wicked deflection off centre-back Morgan, wrongfooting the stranded United keeper as the ball spun over the line.
United had the chance to pull level, Newcastle failed to cut out Treacy's deep cross from the left flank, Jordan Stewart stretched at the far post but powered his header over the target.
Steve Harper produced heroics in the dying minutes as desperate United battled to snatch a late point keeping out Treacy's stinging shot before foiling Henderson.