Chris Wilder's side are 10 points from safety with just three games left following their 25th league defeat of a dismal season.
The basement club, who have only three league wins, will return to the Championship just 12 months after winning promotion.
Anel Ahmedhodzic put the visitors ahead at St James' Park, but Alexander Isak struck twice, Bruno Guimaraes and Callum Wilson each netted and Ben Osborn scored an own goal.
It was the Blades' fourth successive defeat, leaving them without a win in their past 11 games.
Wilder's men have conceded 13 goals in their past three matches, underlining their struggles in season that has appeared destined to end in relegation for months.
They have set a new record for the most goals conceded in a 38-game Premier League season, letting in 97 in 35 games so far.
"We have not been good enough," Wilder told the BBC. "The league has been too powerful for us right the way through the season.
"There's plenty of games where we have been put to bed early but today we should have been 3-0 up at half-time. I'm scratching my head that it was 1-1.
"Newcastle up their game and get a head of steam. Then our old mistakes start to fall in and goals go from two to three to four to five pretty quickly.
"There's a reason why that happens. It's an incredibly young side and there is a complete lack of leadership out there. I thought at times I was going to have a heart attack in terms of trying to get the messages on."
An 8-0 home defeat against Newcastle in September underlined the depth of the task Sheffield United faced in adapting to life in the top tier.
So it was fitting that Newcastle also delivered the final nail in their relegation coffin.
Wilder had already conceded relegation was inevitable after their midweek loss at Manchester United and his fears were confirmed in brutal fashion on Tyneside.
The Bramall Lane outfit have avoided the ignominy of the lowest points tally in Premier League history, which stands at 11, set by Derby in 2007/08.
