Town took the game by the scruff of t he neck in the early stages to earn their advantage with the win just rewards for a fantastci an all-round team performance.
There was a welcome return to the Town starting line-up for Joe Mattock, who had missed the past couple of games through injury. He replaced Rory McArdle in the heart of the defence.
For the hosts, Mark Hughes also made one change from last time out with Lee Angol coming into attack in place of top scorer Andy Cook.
Town came out full of intent and purpose, the energy of the forward causing awkward moments for the hosts back line.
And it was no surprise that they took the lead on nine minutes. A raking cross-field ball from Alex Pattison found Jack Muldoon, who cut inside to beat his man and deliver a pull back to Daly who side-footed home to the right of Harry Lewis.
On 13 minutes Jaheim Headley went into the book for impeding Lee Angol.
Falling behind sparked some lift into the Bantams and on 15 minutes Tyreik Wright had a free-header from the penalty spot but directed his effort well wide and Pete Jameson comfortably watched the ball sail wide.
Wright had another opportunity on 18 minutes when he cut in from the right-hand side and curled an effort just wide of Jameson's goal.
Wright was at the heart of every attacking threat the hosts mustered and at the halfway point of the opening 45 minutes he drove forward and left fly with a fizzing, low strike that Jameson did well to get a faint touch to and deflect behind for a corner.
The home side also forced a couple of corners and they built up the pressure on the Town goal. Mattock then went into the book for hauling back Lee Angol, with the Bantams forward bearing down on the Town penalty area.
Ten minutes before the break Town should have doubled their lead. Danny Grant timed his run to perfection to beat the offside trap and receive the through ball from Alex Pattison. He hesitated at an inopportune time though and ultimately fired well wide.
Goalscorer Daly had a good chance on the stroke of half-time but he volleyed wide of the goal.
With the crowd voicing their displeasure at the break Bantams boss Mark Hughes provided a boost when Andy Cook replaced Harry Chapman for the start of the second half.
Town came out looking to build on the first half performance though and a neat team move freed Headley down the left on the overlap and his effort at goal was deflected wide.
A marauding run from Grant then saw the Town forward hacked down by Brad Halliday, who became the third name to go in the book on the day.
Headley's presence on the left hand side was proving an effective outlet for Town and he had the beating of Halliday to deliver a ball to Muldoon on the edge of the area, with the Town forward striking well at goal but saw the effort cleared for a corner.
The home side had been quiet for the first twenty minutes of the second-half but received a spark when Cook burst forward and freed Dion Pereira, but the Bantams forward sliced wide.
The home crowd were noticeably more vocal now though and got a further lift when Simon Weaver went into the referee's book for something that was said to the fourth official.
Hughes made a triple change on 65 minutes with Ryan East, Scott Banks and Abo Eisa coming on for Angol, Pereira and Wright.
The move almost paid immediate dividends when Town found themselves outnumbered and desperate
defending cleared the lines from a goalmouth scramble.
Substitute banks had a run and shot from the edge of the area that failed to test Jameson but the noise levels in he stadium were rising in anticipation of an equalising goal.
Burrell was then at full stretch to turn away a shot from captain Richie Smallwood as the pressure began to grow.
With five minutes remaining the Bantams played their last card when Vadaine Oliver entered the fray in place of Alex Gilliead.
Simon Weaver then made a double chage as the game entered injury time with Josh Austerfield and Josh Coley rerplaced Muldoon and Pattison.
The hosts continued to press for an equaliser but stalwart defending from the entire Town defence preserved the lead and earned a famous FA Cup victory.
Bradford City: Lewis, Halliday, Platt, Smallwood, Angol (East, 65), Gilliead (Oliver, 85), Foulds, Chapman (Cook, 45), Crichlow, Pereira (Banks, 65), Wright (Eisa, 65).
Subs: Doyle, Songo'o, Odusina, Sutton.
Booked: Halliday (52)
TOWN: Jameson, Ramsay, Burrell, Mattock, Headley, Fakingham, Pattison (Austeefield, 90), Daly, Muldoon (Coley, 90), Grant, Armstrong.
Substitutes: Oxley, Ferguson, Welch-Hayes, Folarin, Horbury, Frost.
Goals: Daly (9)
Booked: Headley (13), Mattock (33), Weaver (63)
Referee: Martin Coy.