Defender Nick Shorey showed Reading's strikers the way to goal as his first ever senior strike decided a one-sided game.
The left-back finally made the break through for the home side 20 minutes from time with a neat finish at the second attempt.
Shorey, without a goal in his 66 previous games for Reading and Leyton Orient, saw a right-foot shot blocked, but made no mistake at the second attempt with his favoured left boot.
The goal was a huge relief for the home side who had dominated through out, but hadwasted a string of chances.
Striker Nicky Forster was the chief culprit. With four goals in his previous three games, the striker was presented with no fewer than nine chances but failed to tuck any of them away.
Forster could have scored a first-half hat-trick, but saw shots fly wide of either post andwas also off target with a free header from a Shorey cross after just seven minutes.
Despite Reading's dominance, their only first-half effort on target was a header from defender Adie Williams, which goalkeeper Steve Banks did well to claw from under his crossbar.
And Banks looked like emerging as the Bradford hero when he saved a Forster penalty on 57 minutes.
Stephen Warnock pulled down Forster in the penalty area, but the striker still could not find a way through to goal as he saw his low spot-kick well stopped by the alert Bantams keeper.
But Shorey finally made the breakthrough after 71 minutes when he drove through a crowded area with a neat finish at the second attempt.
The visitors, who were confident on the back of their impressive win against high flying Norwich on Saturday, had few chances against the lively Royals but midfielder Paul Reid, who struck twice on his first start at the weekend, forced Reading's goalkeeper, Marcus Hahnemann, into a smart low save.
The American keeper was also at his impressive best to beat out a second-half snap-shot by the otherwise redundant Danny Cadamarteri.
The Royals pushed for a second late on, off-colour forward Martin Butler involved in most of the play.
As the game ran into stoppage time the Bantams were allowed a couple of sights of Marcus Hahnemann's goal but were unable to find the target with any of their efforts.
Next up at the Madejski are Reading's old rivals Millwall. Former Royals boss Mark McGhee will hope for a repeat of the sides last meeting, the Lions triumphed 4-3.