Lincoln were hindered by a 63rd minute red card for Mark Stallard before Mark Hudson and Marc Newsham scored for Rotherham.
The Red Imps, looking to stretch their five-match winning streak, started in confident mood against a Rotherham side without a victory in six.
Dodds looked dangerous early on and blazed a first-time effort over the top after an accurate cross from Paul Green.
And home keeper Andy Warrington was forced to produce an excellent save to beat away a stinging shot from Jamie Forrester.
Stallard bulldozed his way through the home defence but then drilled a rising shot over the bar before Warrington was in action again to turn away an effort from Lenell John-Lewis.
In the 25th minute Dodds made the breakthrough when he stole in from the left and snapped up the ball as it broke to him before curling an inch-perfect low shot inside the post out of the reach of Warrington, who may have done a little better.
Rotherham continued to be second best but then they produced an equaliser of impressive quality.
Ian Ross looked poised to shoot from a 25-yard free-kick. But in a brilliantly executed training ground exercise, he clipped the ball into the path of Joseph who met it right on cue with a sweet volley to beat Alan Marriott.
Lincoln were hampered by the dismissal of Stallard after 63 minutes for a sly back-heel that felled Joseph off the ball.
A minute later the home side made the extra man count when they grabbed the lead.
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And in the 73rd minute Rotherham stretched their lead when substitute Newsham (right)latched onto Taylor's throughball and slotted the ball past Marriott with cool precision into the left corner.
Ben Wright pulled one back four minutes from the end on the counter attack but it was too little too late for City as the Millers weren't made to pay for missing a hatful of second half goalmouth chances.