Heung-min Son opened his account for the season with a clinical hat-trick, while the South Korean's deputies James Maddison and Cristian Romero were also both on the scoresheet with blistering strikes from the edge of the box.
Son was an obvious pick as new club captain, but Postecoglou was taking more of a risk in naming Maddison, a summer signing, and the fiery Romero as his understudies.
All three, though, have responded superbly to the added responsibility, raising their games and appearing to embrace the challenge.
As the trio led the celebrations in the front of the travelling fans at Turf Moor, it was remarkable to note how much has changed at Spurs in such a short space of time. Romero by that point wearing the armband, gave it a kiss.
Postecoglou has not just appointed new leaders in the squad, he has ditched the old ones.
Of last season's leadership group, only Pierre-Emile Hojbjerg, who Spurs tried to offload over the summer, is currently part of Postecoglou's plans - and so far only as a back-up.
Hugo Lloris is set to be excluded from Spurs' 25-man Premier League squad when it is named on September 13 despite failing to leave over the summer, while Harry Kane is gone and Eric Dier has been frozen out. The England international failed to make the squad for the fifth consecutive game on Saturday, with 18-year-old centre-back Ashley Phillips named on the bench ahead of him.
Postecoglou, who rarely overcomplicates, has made the point that if Spurs want to change, he needs to enact change, even if that means making difficult decisions. Where his dressing-room leaders are concerned, the Australian's bold calls are so far looking inspired.