Gallagher put the visitors 2-1 up with his second goal of the match before Fernandez sealed the win as Chelsea rallied to secure the points that took them up to 10th in the standings.
The result adds to the pressure on Palace boss Roy Hodgson, whose side have not kept a clean sheet in 13 league matches. They sit 15th on 24 points, five points above the drop zone.
It was a tale of two halves for Chelsea who went into the break a goal down after a superb Jefferson Lerma strike on the half-hourhad given the struggling hosts the lead.
Gallagher’s first goal against the club where he had a spell on loan in 2021-22 came two minutes after the break as he neatly side-footed Malo Gusto‘s cross from the right high into the net.
Another Chelsea counter attack, and another Palmer assist, saw the visitors seal the points in the 94th through Fernandes.
Lerma had put the home side ahead with a spectacular strike from outside the box into the top right corner after Tyrick Mitchell won the ball from Noni Madueke as Chelsea tried to recover from a weak headed clearance by Thiago Silva.
Monday’s result was Chelsea’s 13th consecutive win against Palace in the Premier League – a club record.