His massive effort on Sunday has given the man from Perth the chance of a podium finish next weekend in the celebrated grand tour.
Hindley finished third on the mountainous 15th stage in a sprint finish with the stage winner, Britain's Tao Geoghegan Hart and his Team Sunweb teammate Wilco Kelderman, as race leader Joao Almeida suffered a bad day.
The 24-year-old Hindley was instrumental in helping the trio push to the summit finish together at Piancavallo while the rest of the field suffered - and his efforts have thrown the battle for the leader's maglia rosa wide open.
The 25-year-old Team Ineos rider Geoghegan Hart pointed to the sky after the biggest win of his career and shouted "Nico" as he crossed the line, in tribute to Nico Portal, his team's sports director who died in March.
"I can't believe it ... this team is extraordinary and we are all showing what we're capable of stage by stage," Geoghegan Hart said after earning Ineos' fifth stage win of the race.
"Everyone knows what a great influence Nico Portal had on the team and for me in particular. Every day we ride, we are remembering him."
Almeida collapsed onto the floor with exhaustion at the end of the mountainous 185-kilometre (115-mile) leg from Codroipo to Piancavallo, having had to make a huge solo chase on the first-category climb to the finish, desperate to hold onto the pink jersey.
The 22-year-old Almeida, who rides for the Deceuninck-Quick Step team, managed to finish fourth and remain in the lead but saw his advantage cut to only 15 seconds ahead of Kelderman.
Hindley, who had slumped to 10th overall after Saturday's time trial, had performed so well in backing Kelderman that, though he lost the stage in the sprint by just four seconds to Geoghegan Hart, he is now third overall, 2:56
behind Almeida.
The Giro has its second rest day on Monday before Tuesday's 16th stage, a hilly 229-kilometre (142-mile) route from Udine to San Daniele del Friuli.
The race was rescheduled from its usual May slot because of the coronavirus pandemic. The Giro ends on October 25 with an individual time trial in Milan.
