The Lilywhites banished painful memories of recent EFL Cup and FA Cup exits by sinking Ruben Amorim's injury-hit side at Old Trafford, where James Maddison's first-half goal proved telling.
Spurs' second successive win in the top flight lifted them as high as 12th in the table, further extinguishing any faint fears of relegation after a dreadful start to the new calendar year.
Having also slain Man United 3-0 at Old Trafford in September, when Erik ten Hag was at the Red Devils' helm, Tottenham have now done the double over Man United for the first time in the Premier League era.
Not since the 1989-90 season had Spurs previously defeated Man United in both league fixtures, and the Lilywhites have now got the better of the Red Devils three times this term after December's engrossing 4-3 EFL Cup triumph.
Postecoglou joins elite managers' club in Man United win
As a result, Tottenham are the first team to overcome Man United three times in the same season since Chelsea in the 2012-13 campaign, while Postecoglou is now part of an elite troupe of head coaches.
Having also avoided defeat in both of his top-flight games versus Man United last year, where a 2-0 home win preceded a 2-2 stalemate at Old Trafford, Postecoglou has gone unbeaten in each of his first four Premier League clashes with the Red Devils.
The Australian is just the fourth manager to achieve that noteworthy feat, following in the footsteps of Ruud Gullit, Aston Villa's Unai Emery and Nottingham Forest's Nuno Espirito Santo.
Tottenham were full value for their third win of the season over Man United, having totalled 2.15 Expected Goals compared to 1.54 for the Red Devils, while also enjoying 56.5% possession on the day.
Is Postecoglou eyeing European spots after Man United win?
Postecoglou's men are also vying for Europa League glory between now and the spring, but while the manager is not completely writing off the Premier League season, he has admitted that he is not currently eyeing the European places in the table.
"Considering you guys were asking me about relegation around 10 days ago, I don't think either is where we're looking at," football.london quotes Postecoglou as saying when asked if the continental places were a realistic target.
"I do think the league is tight. What's happened to us is going to happen to other clubs. It's coming. People think I've been making excuses all along, and when I look at what we're doing as just a course of that.
"But trust me, other clubs will feel that as well. It's only mid-Feb. There's a fair way to go. European football for us this year is important this year. We're in the Europa League this year and we've got an opportunity there to make an impact. But I thought we could make an impact in the league. Today was a step towards that."
Tottenham are a whopping 13 points behind fifth-placed Bournemouth and sixth-placed Chelsea and return to action on Sunday away to relegation-battling Ipswich Town.
Written by
Ben Knapton