The experienced part-timer moved to the top of the day's second dedicated co-driver session halfway through the 30 minutes before Warren Luff bumped him to second.
D’Alberto then clocked a session-best 1:20.98s with five minutes remaining to move 0.29s ahead of the Mobil 1 HSV Racing Holden.
"The car felt pretty good there," D'Alberto said. "We just focused on staying out there and getting a bit of tyre temp. It’s extremely slippery, it’s just getting accustomed to conditions, who knows what tomorrow’s going to bring.
"I feel comfortable in the car. This morning we didn’t get to show anything, it’s good to show what we’re capable of.
"Tomorrow’s a new day, everyone’s going to be in the same boat, but we’ve got good cars."
Coulthard paid tribute to his crew for repairing the Falcon between sessions.
"They did a small installation run at the start, just to see if everything’s OK," he said.
"The boys did a great job, they towed it, fixed it and [D'Alberto] did a good job with it, so I’m happy.
"Credit to everyone at Shell V-Power Racing, they’re the ones that turned this car around from my undoing in the practice before, so it’s a good repayment for the boys."
Luff was also happy with his car, which is running a 1994 Peter Brock-tribute livery this weekend, particularly drive onto the long straights.
"The car’s been quite good through sessions so far," he said.
"Around here in the wet it's so slippery, you’re always complaining and asking for more drive.
"When you’ve got the other cars around you and see the struggles some of the other cars are having, I think we’re doing OK so far."
Richard Muscat showed the way early aboard James Moffat’s GRM Holden to end up third ahead of Steve Owen (Supercheap Ford) and Jack Le Brocq (Carsales Nissan).
Triple Eight co-drivers Paul Dumbrell, Steven Richards and Matt Campbell ended up just 14th, 20th and 23rd respectively.
All three had off-track excursions during the session as they struggled to control their Holden Commodores, and Jamie Whincup said that while they weren't running a full wet set-up, there was work to do, even though conditions are forecast to improve on Saturday
"We know we’ve got experienced co-drivers, when they’re down at the bottom, the cars aren’t fast," he said.
"[We] haven’t got any pace, little bit concerning for qualifying tomorrow if the track is wet."