With both sides level on points before the Madejski Stadium match, the winger struck with just over 20 minutes remaining to ensure the Tigers leapfrogged the Royals in the league table.
Reading were without Jimmy Kebe, who was ruled out because of his niggling knee injury, and his place in midfield was taken by Michail Antonio.
Hull also made one change with Brady coming in for Matty Fryatt, who joined new striker Josh King, signed for the club on loan from Manchester United this week, on the substitutes' bench.
Antonio provided the first chance of the match in the third minute when he muscled his way to the Hull byline and crossed for Wales striker Simon Church, who headed wide of Hull goalkeeper Vito Mannone's right-hand post.
Hull endured a sluggish start to the match but Brady came agonisingly close to giving them the lead in the 13th minute when he unleashed a thunderous free-kick from almost 30 yards that Reading goalkeeper Adam Federici did well to tip over the crossbar.
The Royals threatened to break the deadlock in the 20th minute when Kaspars Gorkss met Ian Harte's inswinging free-kick six yards from goal. However, the defender could only head wide of the far post.
Reading continued to press and really should have gone in front three minutes later through defender Alex Pearce, but his close-range effort following Hal Robson-Kanu's corner was superbly blocked on the line by former Royals defender Liam Rosenior.
The rest of the first half was a scrappy affair and aside from some late Reading pressure thanks to successive Robson-Kanu corners and some uncertain handling from Mannone, the closest the game came to a goal was through Hull defender James Chester, whose weak header from Brady's free-kick drifted wide of Federici's right-hand post.
The visitors started the second half with purpose but it was Reading who could have taken the lead in the 52nd minute had Shaun Cummings shown more composure in front of goal. Having been played in by midfielder Jem Karacan 12 yards out, the full-back rushed his effort and lashed the ball high over the bar.
Tigers boss Nick Barmby was the first manager to make a change, introducing Fryatt in place of the ineffective Cameron Stewart after 62 minutes to partner Aaron Mclean in attack.
And the move paid immediate dividends four minutes later as Hull took the lead through the impressive Brady, who ran on to midfielder Paul McKenna's defence-splitting pass and fired expertly from 18 yards past Federici.
McDermott responded by introducing Adam Le Fondre in place of Church but despite the former Rotherham striker's best efforts, Reading failed to create any chances, bringing to a halt their run of four successive home league wins.