Josh Benson handed the Millers a first-half lead but they were denied victory at the Select Car Leasing Stadium by Savage's second goal in as many games.
In-form Rotherham started sluggishly and could have gone behind early on when home striker Kelvin Ehibhatiomhan raced clear.
But although Ehibhatiomhan managed to bypass onrushing goalkeeper Cameron Dawson, he found the angle too tight and shot across the face of the empty net.
Rotherham responded quickly and in the 20th minute, after smart build-up play on the right flank and a clever pass from Denzel Hall, Benson guided a precise effort past Joel Pereira from just inside the area.
Reading, now managed by former Millers boss Leam Richardson, controlled much of the play up until the break but Savage and Ehibhatiomhan wasted half-chances.
The hosts upped the tempo in the second half, with the Millers appearing content to hold on to their lead.
Dawson had to be alert to tip over an audacious 30-yard effort from Savage but could do nothing when, 12 minutes from time, Savage's rasping drive from a similar distance sailed past him.
