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 after Tom Ince earlier struck his 33rd-minute penalty against a post.
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 after 18 minutes.
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.
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 with Davies, who had only been on the pitch three minutes after replacing Conor Sammon, making an immediate impact to volley home Chris Martin's cross.
Adam Legzdins had to save on his goalline from Nathan Delfouneso with five minutes remaining before Davies made two clearances off the line which looked like ensuring the away side 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.
- Sports & Recreation
- Paul Ince
- Tom Ince