Bashir took his first five-wicket haul in only his second Test to help bowl India out for 307 in the morning session of the third day in Ranchi before the hosts fought back, with India needing another 152 runs with 10 wickets in hand to win the match and the series.
Bashir and fellow spinner Tom Hartley, 24, are both still new to Test cricket but shared eight wickets between them in India's first innings.
However, senior Indian spinners Ravichandran Ashwin and Kuldeep Yadav then turned up the heat with nine wickets between them to dismiss England for 145 and tilt the game in the hosts' favour as they chase a winning total of 192.
India lead the five-match series 2-1 but Bashir remained confident of an England victory in Ranchi and then a decider in Dharamsala.
"I know tomorrow I have a job to do and me and Tommy are really excited for the challenge," Bashir told reporters after India made it to stumps on 40-0 in their second innings.
"We saw how Ashwin and Ravindra Jadeja bowled on that wicket, and we take huge confidence from that," he said.
'Very special moment'
Bashir said the challenge to outdo the experienced opposition spinners spurs him on.
"We've still got a bit of a rivalry going on. I used to watch these guys when I was a bit younger and they're world class spinners," he said.
"We know us two lads are up against a world-class attack but we've got a chance to be heroes," he said.
Bashir, who missed the opening match due to a visa issue and made his debut in the second Test in Visakhapatnam, rattled the Indian batting with four wickets on day two during a marathon spell of 31 overs unchanged.
He trapped debutant Akash Deep lbw for his fifth wicket on Sunday and kissed the ground in celebration.
"It was a very special moment on my journey," Bashir said.
"Two years ago, I wouldn't have thought anything like this (would happen)... It was quite emotional as well.
"I lost my two granddads about a year-and-a-half ago and they used to just sit and watch Test cricket all the time. Their wish was to see me out on the TV, I know they're supporting me from up above," he said.
