The Lilywhites arrived at Old Trafford without the services of captain Son, who was deemed unfit following a suspected hamstring problem against Qarabag in the Europa League.
Timo Werner started on the left-hand side of Spurs' attack in Son's absence, as the German combined with Destiny Udogie to keep Noussair Mazraoui and Alejandro Garnacho in check.
Udogie took a knock in the first half of the contest, but the Italy international managed to play through the pain until half time, at which point he was replaced by Djed Spence.
The Italy international started at Old Trafford after playing 78 minutes of Spurs' Europa League win over Qarabag, which was an enforced early substitution due to Radu Dragusin's early red card.
Postecoglou gives positive Udogie injury update
Postecoglou was quizzed on Udogie's fitness in his post-game press conference, and the Tottenham boss confirmed that the left-back had tweaked a muscle in his quad, a slightly worrying admission given that he had surgery in that area at the end of last season.
However, the Lilywhites head coach insisted that his withdrawal was more precautionary than a sign of anything sinister, saying: "Yeah, he was ok," as quoted by football.london.
"I mean he felt something in his quad but he obviously finished the half, but we just thought at half time no point, we've got to be careful about how much we push our players.
"Obviously, Destiny had to come on pretty early on Thursday night, which wasn't the plan and I would say Micky [Van de Ven] played probably more than we wanted him to. So with those kind of things, we just got to be really careful, and Djed did really well when he came on so I thought it was just wise to take him off but we'll see how it goes."
Whether Udogie will be given the green light to face Ferencvaros in the Europa League on Thursday is currently unclear, and the same goes for Son, whom Postecoglou said "just wasn't right" before the game.
Son still doubtful for Brighton & Hove Albion clash
Asked whether Son will be able to face Ferencvaros or Brighton & Hove Albion, Postecoglou replied: "We'll see. Obviously it was a quick turnaround today, so we'll assess it when we go back and get back down to London. We'll see how he is."
While Son's replacement Werner missed two brilliant chances at Old Trafford, hitting two shots straight at Andre Onana while clean through, the German was bailed out of trouble by his fellow attackers.
Brennan Johnson broke the deadlock just three minutes in following an astonishing solo run from Micky van de Ven, before Bruno Fernandes was given a straight red card for a high tackle on James Maddison.
Johnson turned provider for Dejan Kulusevski to strike at the start of the second half, before Dominic Solanke poked in his third goal from three games after Pape Sarr flicked on a Lucas Bergvall corner.
Solanke joined an exclusive club of English Premier League goalscorers with his tap-in at the Theatre of Dreams, as Spurs shot up to eighth in the Premier League rankings and extended their winning streak to four games in all competitions.