The South African blitzed the waterfront Phillip Island circuit with a best lap of one minute and 27.943 seconds.
He did so in fine conditions, but the weather is due to progressively worsen and, with high winds forecast, race organisers brought the 27-lap grand prix forward a day to Saturday to give it the best chance of being run.
The 13-lap sprint was pushed back 24 hours to Sunday, if it is safe to race.
"Safety is the most important factor, for the riders and of course the fans and everyone involved in the event," said Carlos Ezpeleta, chief sporting officer of MotoGP's commercial rights holder Dorna, who called it "a unanimous decision”.
Binder's red-hot time was just shy of the 1:27.767 record Spain's Jorge Martin set last year on his way to pole.
"It was a really good day from the first exit (from the pits) and the bike worked really well," said Binder. "Most important is we're through to Q2 tomorrow and we'll see how we end up.”
World title contender Martin was fourth fastest on his Pramac Ducati, 0.279 behind, with Binder's fellow factory KTM rider Jack Miller second and Aprilia's Maverick Vinales third.
But it was a miserable day for Bagnaia, who struggled for pace and could only finish 11th, 0.699 adrift, meaning he will need to fight his way through Q1 on Saturday.
The top 10 times from Friday's second practice automatically qualified for Q2 and will be joined by the fastest two riders from Q1 to determine the first five rows of the grid both for Sunday's main event and Saturday's sprint.
Among others relegated to Q1 were former world champion Marc Marquez, who crashed on turn 10, and last year's winner Alex Rins.
"I am missing traction on all of the track," said Bagnaia. "This was more or less the issue. The feeling with the bike is not bad, so this is strange.”
Bagnaia out ahead in title race
Reigning world champion Bagnaia is currently 18 points ahead of Martin in the title race with five legs of the 20-stop season left after winning last week's Indonesian grand prix when his key rival crashed out.
Binder was quick all afternoon in Australia, owning the fastest lap of 1:29.365 for almost 40 minutes before Gresini Racing's Fabio Di Giannantonio went a fraction quicker.
That signalled a switch to soft rear tyres and a slew of fast laps with the lead repeatedly changing hands before Martin clocked 1:28.299 to seemingly take control.
But Binder, Miller and Vinales had other ideas and all responded.
In a change of format since the mid-season break, the first practice on Friday had no bearing on Saturday's qualifying order, leaving riders and teams to try out different bike and tyre set-ups without consequence.
In that session, Martin topped the timesheets ahead of Augusto Fernandez and Vinales, with Bagnaia 11th.