Miller, sent on as a sub, had not even trained with his new Shrewsbury team-mates after signing on loan from Sheffield United earlier in the day.
But the striker popped up with almost the last kick of the match to fire a winner after Bradford were unable to deal with Paul Parry's teasing cross from the left.
Shrewsbury enjoyed the better of possession in a goalless first half with Bradford keeper Jon McLaughlin stopping Sam Foley's volley and also pushing out a well struck effort from Asa Hall.
Mid-table Bradford offered little attacking threat, although big striker James Hanson set up Aaron McLean for a volley which was well kept out by keeper Joe Anyon, diving low to his left.
But Bradford took the lead in the 79th minute when defender Andrew Davies stabbed home from close range after Anyon was unable to claim a right-wing cross from Matt Dolan.
Shrewsbury needed a quick response and they got it as Jermaine Grandison's inviting cross was turned home by Jon Taylor, the winger's seventh goal of the season.
Then came the even later drama with Miller's goal sealing a first home win for Shrewsbury since November 23.