The Millers suffered a blow before a ball had been kicked with Lionel Ainsworth injured in the warm-up and replaced by Gareth Evans and more was to follow when Dale Tonge was injured after just two minutes, bringing Mark Bradley into the action as an early replacement.
But it was the home side who dominated the first period. Jake Cole in the Argyle goal made three excellent saves from Evans ,Lee Frecklington and Ben Pringle and Kari Arnason headed home Pringle's 32nd minutes corner, only for the effort to be ruled out for a push.
Argyle could have had a goal in the first minute when Andres Gurrieri's shot flashed wide but their best chance fell to Guy Madjo, who's close-range header in the 39th minute went over.
Again after the break, all the pressure came from Rotherham, but it took them until the 73rd minute to break down Argyle's resistance.
Daniel Nardiello who had a shot saved minutes earlier, broke down the right and from his cross Agard turned the ball home from close range to seal the points.