Goals from man-of-the-match Finn Azaz and a last-gasp winner from Morgan Whittaker, set up by Azaz, gave Argyle their seventh home victory.
The Millers, who took an early lead through Jamie Lindsay, had central defender Daniel Ayala sent off in the 55th minute for a second yellow, but still managed to level through Tom Eaves before Whittaker's late winner.
Argyle boss Steven Schumacher said: "The thing with our lads is because they are young and inexperienced at this level they make mistakes at times, which we can forgive, but what we can never doubt is they never give up and keep going right until the very end.
"I wish it wasn't as eventful but to play nearly an hour in the first half and decisions that were made, to score a penalty and all that, it was quite a draining afternoon.
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