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.
Sammy Ameobi 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.
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 visitors continued to probe - Stockdale making a top-drawer near-post stop to deny Scott McDonald's cheeky flick before Liam 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.