Sean Longstaff, Dan Burn and Sven Botman registered in the first half at Bramall Lane, before Callum Wilson, Anthony Gordon, Miguel Almiron, Bruno Guimaraes and Alexander Isak netted in the second, with Eddie Howe's side having eight different goalscorers in a single match, creating Premier League history in the process.
The stunning result has moved Newcastle into eighth spot in the table on nine points, while Sheffield United sit 20th on just one point from their first six matches of the campaign.
Sheffield United had the first half-chance of the match in the third minute when Luke Thomas found himself free at the far post, but his effort was quickly charged down by two Newcastle defenders.
Just when the visitors were working their way into the match, Magpies head coach Howe was forced into a change, with the injured Harvey Barnes being replaced by Gordon in just the 12th minute.
Thomas had another chance in the 14th minute from a similar position, but he turned his volley from a James McAtee cross wide of the post, with Newcastle given another let-off at Bramall Lane.
The Magpies managed to make the breakthrough in the 21st minute, though, with Longstaff sweeping a cross from Gordon into the back of the net.
There was some controversy about the goal, with the ball bouncing against Gordon's hand, but VAR were happy with the referee's initial decision, and Newcastle were ahead against the run of play.
Gustavo Hamer swept one over the Newcastle crossbar in the 27th minute, before Fabian Schar had a header tipped over down the other end during a lively period of the contest.
The visitors did manage to double their lead in the 31st minute, though, with Burn heading a corner from Kieran Trippier into the back of the net at the far post.
Sheffield United goalkeeper Wes Foderingham made a smart save to keep out an effort from Wilson in the period that followed, but the Magpies made it 3-0 in the 35th minute, with another defender getting in on the act, as Botman nodded a free kick from Trippier into the bottom corner.
The home side were falling apart, and Foderingham had to get down to deny Wilson in the 39th minute, before the two players again locked horns in the 43rd minute with the same outcome.
Foderingham made another smart save to keep out a deflected Gordon effort in first-half stoppage time, with Sheffield United fortunate to only be three goals behind at the break.
Newcastle made it 4-0 in the 56th minute, with Wilson heading a cross from Trippier into the back of the net from close range.
The offside flag prevented Almiron from netting a fifth for the Magpies on the hour, but the visitors had another less than a minute later, with Gordon curling one into the bottom corner from distance.
Newcastle then made it six in the 68th minute through Almiron, who got in on the act by firing into the bottom corner after being released by Guimaraes.
The Magpies had their seventh in the 74th minute through Guimaraes, with the midfielder turning into the back of the net from close range after a deflected shot from Longstaff had fallen kindly for him.
Newcastle's eighth arrived in the 87th minute, with Isak dribbling into the home side's box before carefully finding the back of the net to cap a miserable afternoon for the Blades.
The visitors will now switch their attention to the EFL Cup, hosting Manchester City in the third round of the competition on Wednesday, while Sheffield United will return to league action away to West Ham United next weekend.