The field switched to the hard compound tyre for two more rapid-fire sessions to set the grids for Races 3 and 4.
In both sessions it was the Dick Johnson Racing cars doing battle for pole, the first going the way of De Pasquale, who gapped Davison by just over a tenth.
There was then a healthy half-second gap back to the best of the rest, Shane van Gisbergen, as David Reynolds continued his sparkling form to qualify fourth.
Tim Slade and James Courtney were next ahead of Chaz Mostert and Broc Feeney.
Todd Hazelwood was ninth despite whacking the fence at Turn 5 while Mark Winterbottom rounded out the Top 10.
In the second session Davison was able to hit back in a super tight battle with De Pasquale, the gap between the pair just 0.007s.
"It was really cool," said Davison. "The car was really nice, really well balanced on the hard tyre. You're never quite sure, qualifying on softs yesterday and then having to commit to the lap [on hards], what to do. But the car was super predictable and really well balanced.
"It was down to just ring to get those hundredths out of myself."
Mostert was third fastest while Thomas Randle was the biggest surprise with fourth on what his debut at Albert Park.
Cam Waters was fifth as van Gisbergen slipped back to sixth, followed by Nick Percat, Slade, Brodie Kostecki and Courtney.
