Paul Ince's men made most of the running in the first half but Pool goalkeeper Matt Gilks was forced into impressive saves from Junior Stanislas and Ross Wallace, the former aided by the base of his post.
Sylvestre gave Pool the lead in their 1-1 draw with Nottingham Forest last weekend and he broke the deadlock here with a superb long-range strike after 58 minutes.
Blackpool defended stoutly in the closing minutes, while Tom Ince and Sylvestre almost applied gloss on the counter attack.
The result means the teams share 1-0 home derby wins this term, along with a total of 54 points from 42 games.
Blackpool's on-loan Aston Villa forward Nathan Delfouneso spurned a seventh-minute opportunity to open the scoring, scuffing a shot into the grateful arms of Burnley goalkeeper Lee Grant after Matt Phillips picked him out inside the area.
Seasiders full-back Kirk Broadfoot raided forward to flash a shot past the far post from the right, but Burnley almost took the lead with a quarter of an hour played as Stanislas shot at the end of a driving run to be thwarted by a combination of Gilks and the inside of the upright.
Burnley once again came closest to breaking the first-half deadlock three minutes before the interval. Ross Wallace unleashed a swirling, dipping effort that Gilks did superbly well to touch beyond the crossbar.
After a quiet start to the second half, Sylvestre brought Bloomfield Road to its feet by going one better than Wallace. Little appeared to be on as the French midfielder edged in from the left and curled a wonderful strike into the top corner.
Burnley almost hit back in the 67th minute when Gilks flapped Wallace's cross partially away from the goalmouth but Chris Basham blocked Stanislas' follow-up shot. Blackpool would have been able to breathe easier had Sylvestre not headed wide after Ince's deflected effort came back off the bar.
- Sports & Recreation
- Ross Wallace
- Matt Gilks
- Junior Stanislas
- Paul Ince