Robbie Keane's smart finish in the 15th minute - his 99th goal for us - was enough to book a 4th Round trip to Manchester United on January 27.
Adam Federici produced fines saves to deny Jermain Defoe and Steed Malbranque - the Frenchman's effort cannoned back off the crossbar - while the home side came closest in the 81st minute when Stephen Hunt's dipping volley struck the frame of the goal.
The only concern was seeing Younes Kaboul limp off late on with an ankle injury but coach Gus Poyet indicated later that it wasn't expected to be too serious.
"The most important thing was to get through the tie," said Head Coach Juande at the Madejski Stadium. "We managed to come through the game without conceding a goal and we had to make quite an effort to overcome Reading.
"I was very happy with the performance. Conditions were difficult, the pitch was heavy and we also had very little time to recover after the Chelsea game - there were a few players out there feeling tired and carrying knocks."
Steve Coppell had earlier said we were capable of winning the competition and that point was put to Juande. "We'll try to!" he smiled. "The next tie will be difficult, we go to Manchester United but we'll try our very hardest to go and win that game.
"We have a league game against Sunderland and the Carling Cup semi-final to think about first though."
Are you ready for the Match Day Controlled Parking Zone at White Hart Lane? Starts January 19...CLICK HERE...
Juande Ramos expressed his delight after we overcame Reading 1-0 in Tuesday night's FA Cup 3rd Round replay.