After a confidence-sapping midweek defeat to third-placed Watford, who closed the gap to just one point as a result, the Tigers knew it was imperative they did not crash to a third consecutive home defeat.
And a curious sequence which has seen them win and lose alternate games stretched to a ninth contest when Brady's low 62nd-minute free-kick caught out Middlesbrough goalkeeper Jason Steele, who merely helped it into the net.
Had Hull been able to handpick today's opponents an out-of-sorts Boro side, winless in nine on the road, would have been high on Bruce's shortlist.
Yet if their recent slump was rocking confidence, it certainly did not show in the opening 45 minutes. Sammy Ameobi epitomised that as he waltzed past Corry Evans yet the Newcastle loanee struggled to truly test David Stockdale as his effort lacked power.
Stockdale was then alert enough to stop Mustapha Carayol's deflected cross creeping in at his near post moments later.
In their manager's own words, Hull had lacked a touch of quality in midweek and captain Robert Koren almost answered Bruce's call with a deft touch past Grant Leadbitter before he unleashed a vicious drive which stung Steele's palms.
George Boyd lashed into the side-netting but it was Ameobi, playing just off Ishmael Miller, who continued to impress at the other end.
First he saw a deflected effort go narrowly over the bar and then he picked out Miller with a clever cross which was just too high for the big forward to nod on target.
Alex Bruce, who had earlier come off to receive treatment, succumbed to a right-leg injury on the stroke of half-time to be replaced by Liam Rosenior.
His introduction was followed by Jay Simpson's arrival for the ineffectual Gedo shortly after the break as Bruce deployed a more conventional 4-4-2.
Boro were still asking questions, though, Carayol's effort forcing Stockdale to make a low save down to his right while Miller nearly shook off Abdoulaye Faye outside the six-yard box.
But it was the hosts who finally broke the deadlock just after the hour.
Josh McEachran tripped Koren on the edge of the box and, from the resulting free-kick 25 yards out, Brady struck the set piece low, curving the ball around the wall with Steele only able to push it into the roof of the net.
The Tigers went in pursuit of a second as Republic of Ireland international Brady's next dead-ball delivery was headed over by Ahmed Elmohamady and Simpson screwed wide.
The replacement should have doubled Hull's advantage when Stephen Quinn put it on a plate for him and although his unconvincing strike crawled towards goal, Justin Hoyte still had to hook off the line.
Although the fading Ameobi was withdrawn, Miller remained a constant threat and only James Chester's superb positional sense stopped him heading into an open goal.
The visitors continued to probe - Stockdale making a top-drawer near-post stop to deny Scott McDonald's cheeky flick before Rosenior headed off the line from the subsequent corner.
Hull held on, though, meaning their quest to return to the Barclays Premier League remains in their own hands.