Neither side were able to assert their dominance in the opening stages as the midfielders battled for superiority at Bloomfield Road.
Blackpool took the lead in the 18th minute following a few moments of madness inside the penalty area, as Gary Taylor-Fletcher stroked the ball home after Matt Phillips had seen hit shot cleared off the line.
The visitors were inches away from pulling a goal back midway through the first period but Jamie Ward volleyed wide from 12 yards out.
Derby looked an improved side following the break but they struggled to turn pressure into clear chances.
However, the introduction of Ben Davies made the difference for the visitors as he smashed home a superb volley just moments after coming on.
Derby took control of the contest following the goal and were inches away from taking the lead when Bryson curled an effort wide from the edge of the box.
However, it was Blackpool who snatched the victory in stoppage time when Sylvestre fired in a superb volley.