It was Shane van Gisbergen that led the way in the early stages of the half-hour session courtesy of a 1m02.807s.
Fellow Kiwi Andre Heimgartner then took over top spot with a 1m02.634s before Cam Waters lowered the benchmark to a 1m02.430s.
Friday pacesetter Anton De Pasquale had a brief stint on top mid-way through the session before van Gisbergen went fastest again with a 1m02.258s.
Then with five minutes to go Davison landed the hammer blow, the veteran setting a 1m02.154s despite not running green rubber.
"Really good session, really productive," said Davison.
"We had a good run yesterday, we ran a second set [of green tyres] yesterday. But we knew we were strong on the first set. We wanted to run through the programme and this info overnight helped us a lot.
"We were ready to run a new set [today] but I was happy with what we did re-using yesterday's tyres. We learned what we needed to, there was no point wasting another set."
Heimgartner ended up second, just 0.01s off Davison, while Walkinshaw Andretti United pair Chaz Mostert and Nick Percat were also within a tenth of the pace.
Van Gisbergen was shuffled back to fifth after not improving on his final run ahead of De Pasquale, Waters, Scott Pye, Bryce Fullwood and David Reynolds.
It was a tough session for the two Kosteckis in the field, with Jake Kostecki prompting an early red flag by getting bogged in the sand at Turn 4.
Brodie Kostecki than had a high-speed off at the final corner late in the session, swiping the wall in his Erebus Holden.
"I'm spewing actually," he said. "I was starting to get somewhere with the car and I made a pretty big mistake for the left-handed, got too much kerb and lost it in between both corners.
"It broke the left-rear toe link. Thankfully it's not that bad, but a bit of work for the boys prior to qualifying isn't a good thing."
Qualifying kicks off at 2pm local time.
