Pressley spoke at length this week about how he values culture above all else and said pre-match that he wants his players to play with a "psychological safety".
They did just that in a hugely impressive first-half display, passing out from the back, pressing high up the park and creating several chances.
Joe Bevan dragged his shot wide after a lovely team move unpicked the Rangers defence, Ashley Hay had a bullet header hit the bar, and Ethan Hamilton fired just wide from outside the box.
When Fink pounced on a second ball to score his third of the campaign, no-one at Dens Park could have argued it wasn't deserved.
Even in the second half when they went behind, Dundee continued to battle for every ball.
Led by Owen Bevan and Ryan Astley, they kept themselves in the contest with some brave defending and some excellent saves from goalkeeper Owen Goodman.
Their perseverance paid off as Jones forced an error from Neil and found the bottom corner.
Dundee are fully deserving of their league position after a bright start to the season and Pressley insists there is plenty still to come from this tight-knit bunch.