A curious sequence which has seen the Tigers 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.
If Middlesbrough's 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.
Hull's 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 Robert 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 Jay Simpson screwed wide.
Substitute Simpson 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Although the fading Ameobi was withdrawn, Miller remained a constant threat and only James Chester's superb positional sense stopped him heading into an open goal.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 Liam Rosenior headed off the line from the subsequent corner.