Sylvestre volleyed the Tangerines to safety and sealed a third straight win for Paul Ince's team at Bloomfield Road.
The game looked like ending in a draw after Derby substitute Ben Davies cancelled out Gary Taylor-Fletcher's opener for the hosts.
Manager's son Thomas Ince spurned a chance to give his side a two-goal lead when he struck his 33rd-minute penalty against a post.
Taylor-Fletcher replaced Chris Basham while Blackpool's other change saw Craig Cathcart come in for the injured Alex Baptiste, who is out of contract in the summer and a transfer target for Derby.
Teenage midfielder Will Hughes returned to the Rams' starting line up after two months out with a groin injury, replacing the injured Paul Coutts.
A second change for the visitors saw Adam Legzdins resume in goal for the suspended Frank Fielding.
A driving run into the box from Derby midfielder Jeff Hendrick almost brought a goal after 11 minutes but his shot was blocked by Cathcart.
Taylor-Fletcher tapped in his fifth goal of the season, all of them coming at Bloomfield Road, from close range after Ince picked him out.
The Rams responded well to falling behind and Chris Martin and Jamie Ward both went close shortly before the half-hour mark.
But the hosts were handed the chance to give themselves a two-goal cushion when referee Gavin Ward pointed to the penalty spot following Craig Bryson's challenge on Kirk Broadfoot.
The Derby midfielder appeared to win the ball but the Rams will feel justice was served as Ince's kick struck the upright.
Legzdins made his first save of note at the beginning of the second half, helping Stephen Crainey's free-kick over the crossbar.
The visitors survived another scare in the 50th minute when John Brayford cleared Taylor-Fletcher's shot off the line.
A series of corners resulted in Derby equalising after 65 minutes.
Davies had only been on the pitch three minutes after replacing Conor Sammon. His impact was immediate, volleying home Martin's cross.
Bryson then went close with a curling effort from the edge of the box.
Legzdins had to save on his goalline from Nathan Delfouneso with five minutes remaining before Davies made two clearance off the line which looked like ensuring Derby would earn a point.
However, Sylvestre let fly with a volley from the edge of the box to condemn Nigel Clough's team to a 13th away league defeat.