The Bantams were rewarded for a lively start with a 19th-minute breakthrough as midfielder Payne, on loan from Huddersfield, swept home a low shot from George Miller’s pass after the striker did well on the left.
Shrewsbury, who became the first club in the English Football League or Premier League to open a safe standing area at their Montgomery Waters Meadow stadium, responded well as they chased an equaliser.
Chelsea loanee Charlie Colkett fired narrowly over from outside the penalty area before Kieran Kennedy’s header from Shaun Whalley’s corner was tipped over the bar by goalkeeper Richard O’Donnell.
Whalley then ran at the visiting defence and drilled a 20-yard shot just wide as the hosts ended the first half well.
Shrewsbury, under new manager John Askey, hit the crossbar twice in the second half with midfielder Josh Laurent and substitute Alex Gilliead both unfortunate.
But Bradford also carried a threat with home goalkeeper Joel Coleman saving well from Sean Scannell while Eoin Doyle went close.
Collins said: “It’s an emotional game, whether you’re a player or a member of staff.
“But I said from day one that I have a trust and belief in these players.
“There’s a real togetherness and I see that every day in training.
“I just knew that when the chips are down that men will stand strong and take the fight forward – and that’s what they’ve done.”