Both Shell Fords ran used tyres for the opening laps of the first session, with Davison rolling out on green Soft tyres and sent him back out with just under three minutes remaining.
He retained the same set of tyres for his second stint, and bolted on more greens to shadow van Gisbergen.
Teammate Anton De Pasquale was 18th and seventh in the two sessions.
"We had to throw a lot at the car today, so I enjoyed it at the end there when we got some rewards,” Davison continued.
"We took some really good steps forward and got some good direction. I definitely need more, but I was quite encouraged to see the final time.”
Davison is 274 points down on series leader van Gisbergen in the championship ahead of Saturday’s Race 15.