Stanley had Sean Hessey sent off on 26 minutes with Plymouth then taking the lead with Simon Walton converting the resulting penalty.
It looked all over for them when Ladji Soukouna doubled Plymouth's advantage three minutes into stoppage time at the end of the first half, leaving Accrington with a mountain to climb.
They climbed that mountain without the services of Wes Fletcher, Burnley's other player currently on loan with them. He was sacrificed at half time as John Coleman shuffled his pack and they were back in the game when Long headed in 11 minutes into the second half.
Padraig Amond got the equaliser on 67 minutes to win Accy a point against the league's bottom club in front of a crowd of over 8,000.