Fer produced the only goal of the match eight minutes from time in an entertaining contest in Lancashire.
It looked as though it might prove to be a frustrating afternoon for Swansea, who twice came close early on through their summer signing Fernando Llorente, who was denied on both occasions by Tom Heaton.
The visitors also passed up a glorious chance to score through Federico Fernandez, when he blazed over from three yards out early in the second half.
Burnley had their chances when Andre Gray fired over from the right on 32 minutes, and Dean Marney's deflected strike at the death was superbly saved by Fabianski, but by then Fer had struck the decisive blow after Heaton could only parry Llorente's goalbound effort following excellent wing play on the left by Wayne Routledge.
Read: Burnley match report
Read: Swansea match report