The hosts drew a blank in their opening three home matches in league and cup but finally laid that ghost to rest with a battling performance at the KC Stadium.
Aaron McLean saw an early shot blocked and Brady’s effort was gathered by Adam Federici as Hull pressed.
Nigel Pearson’s side went close with two long-range efforts before half-time but Federici was equal to Brady’s strike and Paul McKenna’s shot drifted narrowly over.
Despite the hosts being on top, Reading sporadically threatened and Jobi McAnuff came within inches of connecting with Robson-Kanu’s searching cross in the 62nd minute.
But it was the hosts who seized the advantage in the 73rd minute when Brady drilled in from 25 yards.
Hull manager Nigel Pearson praised youngster Brady after the Manchester United loanee secured a first home win at the KC Stadium since April 16.
“It’s great for Robbie as he’s been frustrated in training this week,” said Pearson.
“I’m not sure whether he meant the goal, but it doesn’t matter. There is a lot of expectation on him and he is a match-winner.
“He’s young and inexperienced and he’ll make mistakes from time to time, but I’m really pleased with him so far and what he has brought to the squad.”
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