Tottenham took the lead in the third minute at Old Trafford when Brennan Johnson tapped home a cross from Micky van de Ven after the Dutch defender embarked on a solo run from inside his own box all the way to United's byline.
United's battle to get back into the contest took what ultimately proved to be a knockout blow in the 42nd minute as Bruno Fernandes was controversially sent off.
The Red Devils skipper caught James Maddison high with his right foot but slipped as he went into the challenge, although VAR felt referee Chris Kavanagh's initial decision was correct.
Postecoglou's side wasted little time in making their extra man advantage count as Dejan Kulusevski scored in the 47th minute from Johnson's deflected cross.
Solanke was among the goals as Tottenham beat Manchester United 3-0 at Old Trafford
Dominic Solanke added a third in the 77th minute when he gambled on a Pape Matar Sarr header from a corner and poked the ball home.
Tottenham had further chances to add a fourth late in the contest as the game became even more stretched, but it never arrived.
Bent, who made 79 appearances for Tottenham, lauded his former side's defensive work as the visitors were 'absolutely superb'.
'Fantastic from start to finish, caused Manchester United problems,' Bent said on Sky Sports.
'They defended really well. They look comfortable in this system. I think 3-0 does an injustice to Spurs, I think it should have been more. That Spurs performance, absolutely superb.'
Former Manchester United captain Ashley Young offered a more critical perspective on Erik ten Hag's side and was disappointed in the Red Devils' lack of application.
'I think Manchester United didn't give anything,' Young said.
'There was no workrate. Everything was so disjointed.
'Tottenham were so comfortable, United didn't lay a glove on them.
'Tottenham's two centre-halves were moving all over the pitch. It looked like Tottenham were the home team.'
United's 3-0 defeat was their second-straight loss of the same scoreline at home in the Premier League after historic rivals Liverpool dominated proceedings on September 1.
The defeat also heaps pressure back onto Ten Hag as United are winless in three and face a daunting Europa League match against Porto on Thursday before a tricky visit to Aston Villa on Sunday.
As for Tottenham, the win was their second in a row in the league in which they've scored three goals and now sit in eighth on 10 points.