The Seasiders deserved their victory in atrocious conditions, but it was the arrival of substitute Keigan Parker in the 61st minute that turned the tide.
Murphy missed an open goal early in the second half, but he shrugged off the groans of the travelling fans with a great header from Parker' cross for a 64th minute equaliser.
Thirteen minutes later Parker crossed from the left and home keeper Andy Dibble could only palm into the path of Murphy who stabbed home what proved to be the winner.
Woeful Wrexham took the lead in the 18th minute, but it was against the run of play after Blackpool missed several good chances.
Chris Llewellyn was given too much room as he turned and fired home past on-loan shot-stopper Kevin Stuhr-Ellegaard.
Wrexham failed to press home the advantage and Blackpool showed far more urgency and aggression.
To add to the Red Dragons' problems, skipper Darren Ferguson was clearly unhappy with being substituted in the 74th minute and ran straight down the tunnel without acknowledging the bench or the crowd.