Saudi-backed Newcastle had lost three of their opening five Premier League games to dampen expectations of a title challenge on Tyneside.
But Eddie Howe's men showed no mercy as they put the Blades to the sword with ease.
Three goals in 14 first-half minutes set the tone as Sean Longstaff, Dan Burn and Sven Botman put the visitors on course to cruise to victory.
Callum Wilson, Anthony Gordon, Miguel Almiron, Bruno Guimaraes and Alexander Isak were then on target after the break as the Magpies became the first side to have eight different goalscorers, not including own goals, in a Premier League game.
However, they fell just short of the nine-goal Premier League record for a margin of victory.
The size of the defeat sinks Sheffield United to bottom of the table on goal difference with Paul Heckingbottom's future as manager now in doubt.
Brave Spurs battle back
Spurs have still won just once in their last 31 away league meetings with Arsenal, but the optimism garnered under Ange Postecoglou's early weeks in charge was not punctured at the Emirates despite twice falling behind in the north London derby.
"Arsenal are a top team and we had to defend at times. But we showed real courage and bravery to keep playing our football," said Postecoglou.
Arsenal's bright start was rewarded when Bukayo Saka's strike was deflected into his own net by Cristian Romero.
But for the fifth time in seven games under Postecoglou, Tottenham fought back from a goal down.
James Maddison's cross was swept home by Son at the near post three minutes before half-time.
Romero's afternoon went from bad to worse when he was harshly penalised for handball and Saka stroked home the resulting penalty to restore Arsenal's lead.
But the Gunners lost record signing Declan Rice at half-time to injury and that proved costly as an error from his replacement Jorginho gifted Tottenham an equaliser just a minute later.
Maddison was again the creator as he robbed the Italian midfielder and teed up Son for a cool finish into the far corner.
Liverpool cut Manchester City's lead at the top to two points with a 3-1 win over West Ham as Jurgen Klopp's men showed more promising signs of getting back to their best.
The Reds sank to fifth last season, but have the firepower that could make them the biggest threat to City's throne as champions.
Mohamed Salah opened the scoring from the penalty spot after he was upended in the box by Nayef Aguerd.
West Ham's only previous defeat this season came at home to City last weekend and they bounced back to fully merit their equaliser before half-time when Jarrod Bowen's diving header found the far corner.
However, the Hammers were undone by a moment of magic when Alexis Mac Allister's inch-perfect chip picked out Darwin Nunez, who volleyed into the far corner.
Diogo Jota then came off the bench to make it 3-1 five minutes from time.
Mitoma's instant impact
Brighton took advantage of dropped points for both north London sides to move up to third after coming from behind to beat Bournemouth 3-1.
Dominic Solanke fired Bournemouth in front after a glaring error from Brighton 'keeper Bart Verbruggen.
Milos Kerkez's own goal brought Brighton level in first-half stoppage time, but that did not stop De Zerbi sending on Kaoru Mitoma at the break.
The Japanese winger took just 16 seconds to put Brighton in front with a precise finish and Mitoma made sure of the points when he headed home Pervis Estupinan's cross 14 minutes from time.
Chelsea's disastrous start to Mauricio Pochettino's reign goes on as the 10-man Blues lost 1-0 at home to Aston Villa.
Malo Gusto's straight red card for a lunge on Lucas Digne on the hour mark gave the home side a mountain to climb at Stamford Bridge.
Villa made their man advantage count when Ollie Watkins' powerful strike beat Robert Sanchez from a narrow angle.
Despite spending more than any other Premier League club in the summer transfer window, Chelsea have taken just five points from Pochettino's first six league games in charge.
"We need to be aware about what is going on but at the same time we need to be calm," said Pochettino. "We cannot say that the players gave up after 70 minutes, they were fighting until the end with one player less."
