Graham Potter's first win as a manager was controversial, as he was able to ruin Crystal Palace's home debut with a stunning late winner.
Substitute Gallagher, who impressed on loan at Palace last season, curled home a superb right-footed effort to snatch victory for the club.
On his return to the league, Pierre-Emerick had scored his first goal for the Blues after Palace had taken a lead.
There was controversy surrounding the goal as it was set up by Thiago Silva, who Palace thought should have been sent off for a deliberate handball.
Potter brought in Kai Havertz in the 76th minute for the man who earned him his England debut.
With the game seemingly petering out for a draw, the 22-year-old was able to send a curling shot into the top corner.
The Eagles' supporters will likely vent their anger towards the officials after the decision not to send Silva off was made.
The defender appeared to deliberately handle the ball after falling to the ground, denying a goal scoring opportunity.
After a VAR check, the Brazilian was shown a yellow card, which was upheld by the referee, much to the displeasure of Palace's players and their manager.
Palace's sense of injustice worsened when Silva headed James' long ball into the path of Aubameyang, who produced a smart finish on the half-volley.
After the death of Queen Elizabeth II a minute's silence was observed before kick-off and neither side had played in over a month.
The first attack by Palace gave them the lead. Ayew was found on the right by Edouard after he pounced on a pass. Edouard stretched to catch the ball after the Ghanaian's dipping cross.
With their tails up, the home side immediately pressed for a second as Kepa turned Eberechi's shot from distance around the post with the Palace attacker firing narrowly wide from the ensuing corner.
Wilfried Zaha forced a save from Kepa in the second half but Palace were unable to put the Chelsea defence under enough pressure, before Gallagher popped up to rub salt in the home side's wounds.
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