On a fine day ahead of a forecast wet and windy weekend, the South African blitzed the picturesque Phillip Island circuit with a best lap of one minute and 27.943 seconds.
That was just shy of the 1:27.767 record Spain's Jorge Martin set last year on his way to pole.
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 Saturday's sprint race and Sunday's main event.
Among others relegated to Q1 were former world champion Marc Marquez, who crashed on turn 10, and last year's winner Alex Rins.
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, with the Spaniard having to settle for fourth.
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.
