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The visitors had taken a 16th minute lead through an Alan Judge penalty, but Jake Buxton levelled and just when the game seemed to be heading for a draw, Miles Addison headed a winner in the last minute.
It was tough on Plymouth who had been the better side in the first half hour and deserved to go ahead through Judge's penalty.
Judge was tripped by Buxton after Jamie Mackie had hit a post and he drove the spot-kick into the top left corner of Stephen Bywater's net.
Derby had been sluggish but they were level in the 39th minute with Buxton making amends for the penalty.
Roman Larrieu pushed out a Steve Davies header, Robbie Savage volleyed the ball back in and Buxton diverted it into the net.
Derby were forced into a change in the 54th minute when Davies fell awkwardly in the box and was stretchered off to be replaced by Rob Hulse.
The big striker caused the visitors problems and with Derby showing more urgency, Argyle were put under sustained pressure.
But they still had moments at the other end and Mackie gave Derby a real scare in the 85th minute when he got in on the right, only for Bywater to make a good save at his near post.
Mackie was through again in the 89th minute after getting the better of Dean Moxey, but Savage did well to get back and hold him up but the striker should have done better.
That proved to be a turning point because Derby went upfield and forced three corners in a row.
From the third, Gary Teale delivered deep to the back post and Larrieu failed to come for the ball, leaving Addison to power in and head the winner.