© PA Photos
Robinson caused all kinds of problems for the managerless Seasiders, and he gave the hosts the lead on 12 minutes when he found space inside the box and fired into the bottom corner.
The Rams went further in front just after the half-hour mark when Jeff Hendrick found John Brayford inside the box and the defender struck on into the top corner to give them a two-goal cushion at the break.
Blackpool were handed a lifeline from the penalty spot early in the second half, and Thomas Ince made no mistake from 12 yards, but it wasn't long before Derby restored the two-goal barrier.
Robinson tapped home his second of the match on 54 minutes following sloppy defending from the visitors to make it 3-1.
Clough's side dumped more misery on Blackpool on 65 minutes when Conor Sammon got on the scoresheet following neat play from Paul Coutts to condemn Blackpool to a drubbing in the first game of the post-Ian Holloway era.