Jack Stacey's first-half goal proved enough to make it 12 games on the road without defeat, while extending the overall club record for EFL games without loss to 24, as they ground out another vital three points in the bid to win promotion to the Championship.
For a second long away trip in four days, Harford once again named an unchanged starting line-up to that which drew 0-0 at Plymouth on Saturday, with James Shea behind a back four of Jack Stacey, Matty Pearson, captain Sonny Bradley and James Justin.
Alan McCormack anchored the midfield with Pelly-Ruddock Mpanzu and Andrew Shinnie either side of him, and Elliot Lee just behind the front two of Danny Hylton and leading scorer James Collins.
The Hatters made the breakthrough in the 16th minute when Shinnie played a one-two with Lee 30 yards from the Bantams' goal, then played Stacey in on the over-lap and the right-back made no mistake with his shot across Richard O'Donnell into the far corner of the net.
Stacey almost doubled the advantage with a carbon copy straight after, this one saved by O'Donnell, then Shinnie stung the keeper's palms from fully 25 yards before an attempted curler from the Scottish midfielder was off target.
A spell of pinball in the hosts' penalty area led to Lee directing a header at goal from close range in the 22nd minute, but it was straight at O'Donnell.
McCormack went down injured just before the half-hour, and with the midfielder off the pitch - and eventually replaced by Luke Berry - Bradford went close with Hope Akpan's flick from a right-wing corner headed towards the far post, but Nat Knight-Percival couldn't connect with his header at the far post.
Berry was soon into the thick of the action, seeing a 37th-minute shot blocked, then he retrieved Stacey's cross that flew across the six-yard box but saw his half-volley deflected wide for a corner, that Collins' headed wide at the near post.
The Hatters continued to probe but couldn't find that second goal before the break, although they almost had it within 90 seconds of the restart - Berry standing up a lovely left-footed cross from the left that Hylton headed inches over the bar.
Bradford asked a few questions in the Hatters' penalty area, but the defence stood firm - and referee Michael Salisbury as the home fans and players appealed for a penalty as Doyle went down under pressure from Justin - and Collins would have the game's next attempt on goal, twisting and turning in the box before firing a left-footed shot that flew just over.
City responded with a long-range effort from Akpan that went narrowly over Shea's bar, and a scrappy period followed before the Town keeper had to race off his line to cleverly save from David Ball as the Bantams' striker for the wrong side of Bradley and went clear of the Hatters' defence.
The incessant rain and swirling wind were causing issues on a difficult pitch, and home sub Billy Clarke - on for Ball - was next to send a header at goal, but it was well off target and the Town could breathe again as the hosts asked the second half questions.
Harford brought Cornick on for Hylton, and the fit-again striker tried to bend one into the far corner with seven minutes to go, only for the City defence's deflection to take it out for a corner.
The Hatters' other game changer, Dan Potts, was soon raiding down the left and sending an agled shot just over the bar, but with tempers spilling over at times in the final few minutes, the Town were more than strong enough at the back to see the game out.
TOWN: Shea, Stacey, Pearson, Bradley (c), Justin, McCormack (Berry 32), Shinnie, Mpanzu, Lee (Potts 74), Hylton (Cornick 82), Collins. Subs: Moncur, LuaLua, Sheehan, Isted
Goals: Stacey 16
Yellows: Collins, Stacey, Potts
BRADFORD: O'Donnell, Caddis, Chicksen, O'Connor, Knight-Percival, Butterfield, Anderson, Akpan (c), O'Brien, Doyle (Patrick 85), Ball (Clarke). Subs: Wilson (GK), O'Connor, Payne, Maltby, Wright.
Yellows: Knight-Percival, Anderson
REFEREE: Michael Salisbury
ATT: 15,992
AWAY: 1,044
