Goddard put the Triple Eight wildcard entry on top with a 1m09.640s five minutes from the scheduled conclusion of the half-hour co-driver practice.
He then improved on the very next lap with a 1m09.310s.
That put the #888 entry three-tenths clear of Richie Stanaway in the fellow T8 car that he'll share with Shane van Gisbergen.
There was no scope for anybody to improve once Goddard had done his lap, too, with Jake Kostecki dislodging a cone at turn 6 which led to the session being red flagged and never restarted.
"I made a bit of a mistake at the back corner, so there's definitely a bit of time in it," said Goddard. "But the car is feeling really good. It's a positive way to start. We've still got another practice this arvo so we'll keep building on it."
Jamie Whincup made it a Triple Eight top three lock-out with the third-fastest time, while Lee Holdsworth was the best-placed Ford in the Walkinshaw Andretti United entry he'll share with Chaz Mostert.
Jayden Ojeda was fifth quickest in the lead Matt Stone Racing entry as Jono Webb was sixth fastest on his return to Supercars.
Micheal Caruso was sixth for Team 18 ahead of Erebus pair Jack Perkins and Dave Russell, with Jaxon Evans rounding out the top 10 for Brad Jones Racing.
Zak Best, meanwhile, prompted an early red flag in his Tickford Racing entry after going off at turn 9.
At the back end of the top 20 was Porsche star Kevin Estre, who was taking part in his first official Supercars session for Grove Racing.
"Great, a really good old school track," he said of his first taste of Sadown. "It's very tough with this car and the rear tyre drops quite early in term of grip, so the more laps you do, the better I drive, but the worst I am in lap time, which mentality is not so easy."
Friday's action concludes with a third half-hour practice session, open to all drivers, at 3:45pm local time.
