Championship leader Marco Bezzecchi conceded the top spot to Bagnaia in the standings when he crashed with seven laps to go while Binder also moved up three places to third in the table.
Bagnaia has a 22-point lead over Bezzecchi after four rounds while Binder is a further three points behind.
Binder's teammate Jack Miller finished third to move up to fourth in the riders' standings.
The two KTMs had a superb start as Saturday's sprint winner Binder and Miller led into turn one but the race was red-flagged after Yamaha's Fabio Quartararo and RNF Racing's Miguel Oliveira crashed on the opening lap.
Oliveira was declared unfit to resume after dislocating his shoulder, marking the second time this season he was forced to abandon the race after Marc Marquez crashed into him in Portugal last month.
It was deja vu on the restart as the KTMs surged into the front with Binder making up three places by turn one to take the lead with Miller and Bagnaia behind him.
Bagnaia and Miller were involved in some aggressive racing with the Italian forced to drop a position by race control after moving up to second when he nearly took out the KTM rider on an overtake that left the Australian fuming despite an apology.
A mistake from Miller opened the door for Bagnaia and the world champion charged after Binder with nine laps to go, setting the fastest lap as he looked to reel in the South African.
Bagnaia's determination reaped dividends when he finally got past Binder with three laps to go and although the KTM rider threw everything at him and closed the gap on the turns, the Ducati rider held him off to take the chequered flag.
Meanwhile, Quartararo's day went from bad to worse when the 2021 champion, who was penalised with a long-lap penalty for the crash, was forced to repeat it as he eventually finished 10th
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