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Debutant Dickinson, who joined the Tangerines on loan from Derby County on Thursday, scored with his first touch to level the scores in the 78th minute after Paul Gallagher's opener for the home side.
Three minutes later, Dickinson netted again to send the small band of away fans who had made the long trek south back to Lancashire happy.
A lacklustre game was brought to life midway through the second half when Plymouth substitute Steve MacLean played Gallagher and the on-loan Blackburn attacker curled a lovely shot past goalkeeper Paul Rachubka from the edge of the penalty area.
MacLean continued to make an impact and should have put the match beyond Blackpool's reach when Gallagher crossed from the right, but his header was glanced wide of the post.
Argyle were left to rue the wasted opportunity ten minutes later, after Dickinson had come on for Steve Kabba.
First, the former Stockport County man outmuscled Argyle skipper Marcel Seip to reach Ben Burgess' header into the penalty area and fire past goalkeeper Romain Larrieu.
Within three minutes, Dickinson score again, seizing his opportunity after fellow debutant Kyel Reid, who had also joined Blackpool on loan - from West Ham - on Thursday, had made ground down the right flank.
Reid's cross was low and hard to the near post, to where Dickinson had timed his run perfectly to beat Craig Cathcart to the ball and slam home the winner.
The spectacular final quarter of the game was in complete contrast to what had gone before, with neither side able to grasp the initiative and neither goalkeeper being tested.