Binder, on a KTM, finished 0.48sec ahead of Bagnaia on a Ducati. Bagnaia cut Italian compatriot Marco Bezzecchi's lead in this year's standings after the Mooney-Ducati rider collected just one point for eighth.
Spaniard Aleix Espargaro, who had dominated practice and qualifying for two days, crashed his Aprilia on the sixth lap.
Binder and Bagnaia had finished outside the top 10 in practice and had been forced to ride in the opening qualifying earlier in the day where they grabbed the last two spots in the shootout for the first four rows on the grid.
They made the most of their second chances by grabbing places on the second row of the grid in the last qualifying session.
Starting from the fourth position was Binder, who also won the sprint in Argentina. After KTM team-mate Jack Miller, who started on the front row, seized the early lead, Binder and Bagnaia gave chase. They overtook the Australian in the last two laps.
Ducati-Pramac's Jorge Martin, who put pressure on Bagnaia for a long time without managing to overtake, finished fourth ahead of Portuguese Miguel Oliveira (Aprilia RNF)and Spanish veteran Daniel Pedrosa (KTM).
The race was interrupted on the first lap after an accident caused by Franco Morbidelli (Yamaha) brought down Bezzecchi and Spaniards Alex Marquez (Ducati-Gresini) and Augusto Fernandez (KTM-GasGas). The four riders were unharmed.