Calvin Zola gave the hosts a first-half lead but Harrad struck with his third goal in as many games on loan from Bury to rescue a point and leave the Brewers without a win in eight games.
Burton had the better openings after a sluggish start, but had to wait until five minutes before the break for their opener.
Jacques Maghoma fired too high after a powerful run from midfield and Adam Bolder had a shot blocked after dwelling too long on a chance inside the Rotherham box.
Andres Gurrieri then drove a shot too close to goalkeeper Rhys Taylor.
The hosts were finally rewarded when Zola got the final touch to a John McGrath free-kick which deceived the visitors' defence at the near post.
Bolder spurned a chance to extend Burton's lead but the Millers came out on top after the break and it proved a costly miss when Rotherham deservedly levelled in the 56th minute.
Sam Wood drove in a corner low across the goalmouth and Harrad was on hand to bundle the ball over the line.
Burton had a chance to win it near the end but Zola fired into the side-netting after rounding goalkeeper Rhys Taylor, who then kept out a blistering shot from Bolder in added time.
Source: DSG