Brennan Johnson's early goal knocked the stuffing out of the home side, who lost captain Bruno Fernandes to a straight red card before half-time.
Dejan Kulusevski and Dominic Solanke scored in the second half to underline Tottenham's total dominance against their disjointed and indisciplined opponents.
It was United's second straight 3-0 defeat at home in the Premier League after Liverpool hammered them earlier in September - leaving them 12th in the table with just two wins from their opening six games.
The club's haul of seven points equals their worst record at this stage of a Premier League campaign, and they have scored just five times.
Former United captain Gary Neville, now a TV pundit, tore into his former team, describing Sunday as a "shocking and sobering" day for Ten Hag's men.
"It was an absolutely disgusting performance in that first half in effort, quality, everything you would want in a football team," he said on Sky Sports.
"There will be a lot of questions to answer for that group (of players) and the manager in the next week."
Former Liverpool and Spurs midfielder Jamie Redknapp said United had "no identity".
"It gets to a point where you feel for the manager," he said. "He looks completely out of his depth and is struggling to motivate.
"It was so easy for Tottenham, they were so comfortable, so calm. Man Utd are going backwards, he can't complain any more. They have spent over £600 million and have his defenders in.
"They are rock bottom and I don't see where they can go from here."
On the brink?
Last season Ten Hag could legitimately point to a lengthy injury list, especially in defence, as a factor in his team's struggles.
But aside from the missing Luke Shaw, they currently have few players missing and Ten Hag strengthened his squad during the summer transfer window - taking total spending during his tenure to more than £600 million.
Now into his third season at Old Trafford, the argument that the team are still a work in progress looks increasingly weak.
Liverpool, after all, are top of the league just six matches into the Arne Slot era.
Of equal concern for United fans is that the team, as Redknapp points out, show few signs of establishing any sort of identity, often proving less than the sum of their parts.
Former England striker Alan Shearer, speaking on The Rest Is Football podcast, said: "Can anyone tell me what Manchester United are?
"What is their system? What is their plan? Do they sit, do they attack, do they press? I don't know. I don't have a clue what they are. They are a mess."
A defiant Ten Hag, who survived a post-season review by club bosses, partly thanks to a shock FA Cup final win against Manchester City, says he is not worried about his future.
"We need some time," said the Dutchman. "We are all on one page or in one boat together, the ownership, the leadership group, the staff and the players group as well. I don't have that concern."
Whether he gets that time or not might depend on whether he can inspire his beleaguered men in tough matches against Porto and Aston Villa in the coming week.
United co-owner Jim Ratcliffe shows no sign of immediately pulling the trigger, with reports suggesting the club hierarchy will continue to support their embattled manager in the short term.
Ten Hag may not be "sacked in the morning" as Spurs fans gleefully predicted, but he knows it is now or never as he fights to save his job.
