Leandro Trossard's opening strike was followed by own goals from Ruben Loftus-Cheek and Trevoh Chalobah as rambunctious Albion sprinted to a dominating lead by halftime.
Just after the break, Kai Havertz scored to give the Blues some hope, but Pascal Gross' injury-time goal sealed the Blues' first loss in 10 games following Thomas Tuchel's dismissal.
The Seagulls' extraordinary triumph at the boisterous Amex Stadium was their first under new head coach Roberto De Zerbi and their first victory over the west London club since 1933, with the harsh home fans enthusiastically taking pleasure in their ex-manager's agony.
The Albion team entered the day with just two points from a potential 15 since Potter's departure seven weeks ago. Potter, who left Stamford Bridge with six victories and three draws from nine matches, was looking to exact more punishment on the Albion team.
When he got off the team bus, there were jeers and a few cheers, and when he came out of the tunnel, there were more jeers.
Brighton benefited from the angry spirit of their supporters and swiftly took control of the game during a fast start.
While three sides of the stadium exploded in the fifth minute, Chelsea captain Thiago Silva had already twice been compelled to head off his own goal-line, first to deny Trossard and afterwards Pervis Estupinan.
On his complete Premier League debut, Japanese winger Kaoru Mitoma earned the assist by deftly dancing into the area and offloading to the hot-shot Trossard, who rounded goalkeeper Kepa Arrizabalaga and powerfully slammed his seventh goal of the campaign past former Seagulls defender Marc Cucurella.
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And with 14 minutes remaining, Albion duly increased their lead, leaving Potter in the away sideline looking shocked.
Recalled midfielder Loftus-Cheek could only deflect Solly March's inswinging corner from the right into his own net by hitting the underside of the crossbar.
There was a thunderous commotion within the stadium as a result of the swift goals, with cries of "Potter, what's the score?" getting louder and being followed by joking inquiries about the future of his employment.
Chelsea had a terrible start, but they weren't discouraged, and as the intense, end-to-end battle went on, they had multiple opportunities to cut the lead in half.
After Robert Sanchez stopped Conor Gallagher's original shot, Christian Pulisic surprisingly missed the goal with the opportunity still present.
When Gallagher's flicked header hit the woodwork, Spain's Sanchez made an incredible one-handed diving save to divert the ball over the bar.
Raheem Sterling was later denied a penalty after falling down in response to Gross' tackle, while Havertz was also barred from the game.
Three minutes before halftime, Chelsea once more contributed to their own demise, putting an end to any burgeoning momentum for the visitors.
This time, a charging full-back named Estupinan cut the ball back to the left, and slipping Chalobah caused harm by deflecting the ball past Kepa.
For the second period, Potter substituted goalkeeper Kepa with Edouard Mendy owing to an apparent injury, but he soon had cause for greater hope.
Loftus-Cheek laid the ball off to Gallagher, who then supplied an excellent cross from the right, and Havertz slipped through Albion's defense to head home unchallenged.
Prior to Potter suspending the unproductive Sterling and Brighton's player of the season for 2021–22 Cucurella and the introduction of Ben Chilwell and Pierre-Emerick Aubameyang, Sanchez stopped a Gross own goal as the Blues pushed for yet another goal.
After a bright replacement named Julio Enciso was stopped by Mendy, Gross poked in on the rebound to send Chelsea home humiliated despite controlling the game for the majority of the final 25 minutes.
On a discouraging afternoon for his successor Potter, Italian De Zerbi joyfully celebrated a momentous occasion with his new supporters.
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Potter