Rangers played for nearly 50 minutes with 10 men after winger Hogan Ephraim was dismissed for an ugly lunge on Jimmy Kebe at the end of the first half, but struck with eight minutes left to move a step closer to promotion.
Reading had been on the back foot for the opening half-hour but rallied to create the best chances either side of the red card.
But Neil Warnock's side refused to sit back in the second half and claimed the three points when Routledge capped a rare move of quality with a fine low finish.
Warnock is looking for the seventh promotion of his managerial career but was furious with the decision to dismiss Ephraim and was lucky not to be sent-off himself.
His side should have had a fifth-minute lead when right-back Bradley Orr was given far too much room to send in a cross which Rob Hulse should have sent on target instead of heading wide.
Playmaker Adel Taarabt looked the most likely source of a goal and he came close with a strike from 25 yards which was over the top after good play from Alejandro Faurlin on the left.
Reading had hardly been out of their half for 10 minutes but Simon Church then tested Paddy Kenny with a fine strike on the half-volley.
The home crowd were revived and from the corner Matt Mills saw his header at the far post well saved by Kenny, while Simon Church could not smuggle the rebound over the line.
The momentum was all Reading's and Ephraim was soon back in the changing rooms.
He looked to break after a knock down from Hulse but his touch let him down and the winger lunged dangerously in on Kebe in his efforts to retrieve the ball and was shown a straight red card by referee Russell Booth.
Warnock was far from happy and his side were in danger of losing their cool as several players from both sides crashed into challenges.
Shane Long should then have scored just before the break when Kenny misjudged a bouncing ball, but the Republic of Ireland international hit the side-netting from an acute angle.
Warnock sent out his 10 men after the break and to his credit pushed Taarabt right up alongside Hulse.
Mills almost stole onto a quick free-kick from Ian Harte as the game hit a lull, before an already angry Warnock hit boiling point when Reading midfielder Jay Tabb was not booked for a cynical foul on Taarabt.
The former Sheffield United manager was lucky not to join Ephraim in being dismissed after hurling a water bottle in frustration.
Booth was back in the spotlight on the hour mark when Long went down under a challenge from Orr inside the box but the referee this time waved away the protests.
The game looked set for a goalless draw until Rangers stole the points with an 82nd-minute winner.
Inevitably Taarabt was involved and after he turned well on the left and found Faurlin, the Argentinian released Routledge in on goal with a perfect through pass.
The Newcastle loanee had plenty to do but drove his shot firmly past Adam Federici and into the bottom corner to send the points home to Loftus Road.