The Royals started the game well as Kelvin Ehibhatiomhan had a header cleared off the line before his side then took the lead thanks to a beautiful strike by Savage.
The midfielder received the ball in the left corner of the box and sweetly struck home with his right foot into the far side netting for his first goal of the season.
Reading came close to doubling their lead on the half-hour mark as Lewis Wing whipped in a cross from the right and found Jeriel Dorsett who just lifted the ball over the crossbar with a mis-hit effort.
Just before the break the referee pulled out a red card for the previously booked Dorsett but, after a conversation with his assistant, it was adjudged a case of mistaken identity and Daniel Kyerewaa received a caution instead.
Stevenage started the second half much better than they did the first and had a great chance to level the game but the woodwork came to Reading's rescue.
Royals full-back Kelvin Abrefa played a backpass that was poorly judged and put Boro striker Ahadme through on goal and he took a touch to the right before letting fly with a shot that crashed against the crossbar.
That would prove to be as close as Stevenage would come to an equaliser, although Reading keeper Joel Pereira did make a fine double save from Dan Kemp and Phoenix Patterson, as the hosts gamely held out.