Postecoglou's team won 2-1 away to Ferencvaros to maintain their winning start to their Europa League campaign.
Pape Matar Sarr put Tottenham ahead before Brennan Johnson added another goal late on, with the visitors prevailing despite Barnabas Varga netting for Ferencvaros.
The win saw Postecoglou match a feat that Jose Mourinho previously achieved as Tottenham manager.
Even Antonio Conte, who was in charge from November 2021 to March 2023, couldn't match that sequence.
Ange Postecoglou achieved a significant feat as Tottenham beat Ferencvaros 2-1
After overcoming Ferencvaros, Postecoglou has now overseen five consecutive wins for Tottenham across all competitions.
That followed on from successes against Manchester United (Premier League), Qarabag (Europa League), Brentford (Premier League) and Coventry (Carabao Cup).
As reported by Squawka, the last time that Tottenham enjoyed such an impressive run was between February and March 2021, when Mourinho was in charge.
In that run of games, Tottenham won against Wolfsberg, Burnley, Fulham, Crystal Palace and Dinamo Zagreb before losing away to Arsenal.
Postecoglou's team will be looking to keep their winning run going when they face Brighton away on Sunday.
In addition, Postecoglou will hope to fare better than Mourinho by winning a trophy during his time in charge of Tottenham.