Anel Ahmedhodzic gave the visitors a deserved early lead, nodding home Gustavo Hamer’s inswinging cross from close range.
The Blades carved out several opportunities to double their advantage as Newcastle struggled to gain a grip on proceedings, but the home side were level when Alexander Isak drilled home from Jacob Murphy’s pass in the 26th minute.
Ben Brereton Diaz had a goal-bound shot blocked by Dan Burn and Mason Holgate headed against the woodwork on the half-hour mark, but the visitors fell behind early in the second half when Bruno Guimaraes steered Lewis Hall’s delivery into the far corner.
Isak registered his 23rd goal of the season from the penalty spot after Anthony Gordon was brought down by Holgate, before the unfortunate Ben Osborn bundled into his own net for Newcastle’s fourth.
Callum Wilson came off the bench for the hosts to score his first top-flight goal since October.
Sheffield United were awarded a late penalty, but the decision was overturned by the video assistant referee who ruled Magpies substitute Alex Murphy had won the ball in a challenge with Jayden Bogle.
The defeat leaves the Blades 10 points adrift of safety with only three games remaining, while Newcastle stay seventh and are well placed to secure a spot in Europe next season.
The writing has been on the wall for quite some time for Wilder’s side, who started brightly on Saturday but fell to pieces after Guimaraes gave Newcastle the lead.
The Blades have been stuck in the bottom three since late September, when they were thrashed 8-0 by Eddie Howe’s team at Bramall Lane in their record league defeat.
Only Swindon Town have conceded more goals in a single Premier League season than the Blades, who have now shipped 97 goals in 35 games.
The visitors enjoyed plenty of early possession and could have doubled their lead after Ahmedhodzic’s early opener, with Cameron Archer having a shot deflected wide following a mazy run.
Archer then had another effort blocked by Burn, who was in the right place at the right time to prevent Brereton Diaz putting the visitors back in front after Isak’s leveller.
READ ALSO: Onana costs Man Utd as Burnley grab draw
Holgate was denied by the frame of the goal and Andre Brooks skewed a long-range effort wide early in the second half, but Newcastle never looked back after Guimaraes’ header.
Referee Tony Harrington awarded the visitors a late spot-kick after Bogle went down under pressure from Alex Murphy, but Wilder’s team were denied a late consolation after VAR ruled the Newcastle defender had got his toe to the ball.
If the home supporters were expecting a fast start from the Magpies after Wednesday’s limp defeat at Crystal Palace, they were left disappointed.
Howe’s team are aiming to secure European qualification for the second season in succession but started the game as if they had little to play for, with the visitors dominating possession and first to every loose ball.
Newcastle failed to kick on after Isak’s equaliser but very nearly completed the turnaround on the stroke of half-time, but Wes Foderingham got a strong left hand to Hall’s low drive from the edge of the box.
However, the hosts finally took control after Guimaraes’ fifth goal of the campaign and could have added even more gloss to the scoreline after Wilson made it 5-1.
Newcastle have scored 13 league goals against the Blades this season – the most one team has registered against another in a single Premier League campaign.
In-form Isak has found the net in his past seven appearances at St James’ Park – only Andrew Cole and Alan Shearer have enjoyed longer streaks for the club.
Newcastle are now four points clear of eighth-placed West Ham with a game in hand and just a point behind Manchester United in sixth, after the Red Devils conceded a late equaliser at home to Burnley on Saturday.
