The Magpies initially made a sluggish start to the contest and fell behind in the fifth minute when Anel Ahmedhodzic nodded the visitors into a deserved early lead.
However, in-form striker Alexander Isak restored parity for Newcastle with a low-driven strike just before the half-hour mark, and the floodgates then opened after the interval.
Bruno Guimaraes put the Magpies ahead in the 54th minutes after steering Lewis Hall's delivery into the far corner, shortly before Isak's converted penalty and an own goal from Ben Osborn put the hosts in cruise control.
Callum Wilson completed the rout on the 72-minute mark with a goal just six minutes after coming off the substitutes' bench, securing maximum points for Eddie Howe's side and confirming Sheffield United's relegation back to the Championship.
Newcastle relegate Sheff Utd with clinical display
Newcastle have completed their first league double over Sheffield United since the 2019-20 campaign and have done so in emphatic fashion to set a new Premier League record.
The Magpies celebrated their biggest-ever Premier League victory when they thrashed the Blades 8-0 in the reverse fixture at Bramall Lane in September last year, setting multiple records in the process.
Five more goals scored on home soil against Chris Wilder's side on Saturday means they have netted a total of 13 goals across just two games versus the South Yorkshire outfit, the most goals one team has ever scored against another in a single season in the division's history.
Isak has scored three of those 13 goals for Newcastle, with his brace on Saturday increasing his total for the season to 19 in the Premier League, just one behind both Erling Haaland and Cole Palmer (20 each) in the race for the Golden Boot.
The Sweden international has continued his magnificent scoring run at St James' Park, netting in each of his last seven home league games with only Alan Shearer (15 in May 1997) and Andrew Cole (eight in February 1994) having enjoyed longer streaks for Newcastle.
Isak targeting European qualification with Newcastle
Newcastle have bounced back from their midweek defeat at Crystal Palace by beating Sheffield United and have consolidated seventh place in the Premier League table, sitting four points ahead of eighth-placed West Ham United, who have played a game more and drew 2-2 with Liverpool earlier in the afternoon.
Isak was delighted to contributed to the Magpies' latest triumph over the Blades and is targeting a strong finish to the campaign as they endeavour to qualify for European competition.
"I'm very happy. It was important for us to stay in the race for Europe," the 24-year-old told Premier League Productions. "We got off to quite a bad start and needed one goal against us to wake up. The reaction was very good. The manager gave us a wake-up call at half time.
"Many of my penalties have been here at home. I tried to stay calm and focus on the moment. I was thinking I want a hat-trick. I haven't had one.
"Europe is still alive and we have to focus on ourselves and we'll see how it goes."
Newcastle, who have collected 13 points from their last six matches, will look to claim three more when they play host to Burnley next weekend, before ending the season with fixtures against Brighton & Hove Albion, Manchester United and Brentford.