Harrad sparked a second half comeback to earn a point for the Brewers.
To be fair it was no more than they deserved after some decent attacking football throughout, as Rotherham's clinical finishing and any kind of rhythm of play deserted them in the second period.
The Millers took the lead in just the second minute when Kevin Ellison's 25 yard free-kick found its way past Adam Legzdins.
Despite Burton's decent passing and approach play the Millers made it two on 34 minutes, Ryan Cresswell heading in Exodus Geohaghon's long throw.
And it was 3-0 and seemingly game over just before the break as Adam Le Fondre expertly converted Ellison's right wing cross from close range.
The second half however was a total turnaround as Burton struck back immediately.
A mix up between Cresswell and Keeper Andy Warrington allowed Harrad to tap into an empy net.
Harrad then netted his second from the spot after Johhny Mullins tripped Jimmy Phillips in the box and the striker fired in past Warrington as Rotherham looked disjointed.
And the comeback was complete with seven minutes left as Greg Pearson and Harrad combined with some neat interplay, Harrad sliding the ball into the corner to the delight of the visiting support as the Millers were booed off.