The visiting Bantams looked down and out at half-time after goals from Peterborough’s Ivan Toney and Siriki Dembele.
But Kevin Mellor and substitute Luca Colville secured a dramatic draw, by scoring in the 84th and 89th minutes to ensure Bradford’s place in today’s draw.
“We conceded two very poor goals and gave ourselves a mountain to climb,” admitted Hopkin. “That’s a massive performance from us. The mindset here is changing and I think everyone can see that.
“I said to the players at half-time to make sure we were in the hat on Monday.”
Bantams’ stopper Richard O’Donnell produced fine saves to deny Toney and Ryan Tafazolli, who did well to get on the end of Marcus Maddison’s free-kick. But the opener came with Bradford being caught on the counter as Toney buried Maddison’s cross.
Toney turned provider for the second by playing Dembele in behind before the 22-year-old calmly fired home.
Just after the break Eoin Doyle’s strike was thwarted by an outstretched Aaron Chapman.
On the hour O’Donnell pulled off another top stop to tip Maddison’s effort wide.
Right at the death Bradford turned the tide in dramatic fashion.
Mellor’s unstoppable 30-yard strike, a memorable first goal for the club, gave Hopkin’s charges a mere glimmer of hope before Colville salvaged a draw late on.
Peterborough United: Chapman, Ward, Tafazolli, Bennett, Daniel, Maddison, Reed (O’Hara, 86), Woodyard, Dembele (Naismith, 70), Godden (Cummings, 79), Toney. Unused substitutes: Denton, Bassong, O’Malley, Cooper.
Bradford City: O’Donnell, Caddis, O’Connor, Mellor, Chicksen, O’Brien (Colville, 64), Henry (Brunker, 78), Ball (Miller, 64), O’Brien, Payne, Doyle. Unused substitutes: Wilson, McGowan, Devine, Wood.
Referee: T Kettle (Notts).