Brighton were rampant, merciless and utterly brilliant. They exhibited many of the better traits of their former manager, playing with style, intelligence and tactical flexibility, but this was no tribute act. It was Potterball with a De Zerbian flourish and, as Chelsea left the pitch to the sound of mockery ringing in their ears at full-time, nobody inside the Amex Stadium could have made the mistake of thinking that Brighton were pining for the past.

There was no room for any sentiment. Watching from an unfamiliar spot in the away dugout, Graham Potter found himself powerless to silence the jeers. Nothing was going to deny Roberto De Zerbi his first win as Brighton’s manager and, once the dust had settled, it was left to Potter to question his tactics, wonder why control had eluded Chelsea and even suggest that his use of Raheem Sterling and Christian Pulisic as wing-backs had left him looking “a bit of a fool”.

Related: Graham Potter admits he looks ‘a bit of a fool’ after Chelsea’s defeat to Brighton

It was an agonising way for the former Brighton manager’s nine-match unbeaten run to end. Potter’s former employers were out for revenge and they ruthlessly exploited Chelsea’s frailties. De Zerbi had his team geared to attack down the flanks, where the positioning of Sterling and Pulisic exposed an overworked back three, and the approach bore fruit during an opening period that ended with Chelsea grateful only to be 3-0 down.

For De Zerbi, who had gone five games without winning since replacing Potter, it was vindication of his attacking philosophy. “We played a fantastic game,” Brighton’s manager said. “We played with courage.”

There was anger, too. The curious back and forth between these clubs had the home fans baying for blood from the start. There were jeers for Marc Cucurella, vitriol for Potter and his coaches, and the venomous atmosphere lifted Brighton, whose overriding aim appeared to be forcing anyone tempted to call them Chelsea’s feeder club to think again.

The week, after all, had started with Chelsea looking to hire Brighton’s director of recruitment, Paul Winstanley. The dynamic has felt dispiriting, a member of the elite using their deep pockets to outmanoeuvre a smaller rival, and Brighton had a point to prove.

Their football blew Chelsea away. Thiago Silva, whose distribution from the back was poor, made goalline clearances from Leandro Trossard and Pervis Estupiñán during the opening minutes, and the visitors soon cracked. Slack play in midfield allowed Kaoru Mitoma to find Trossard, who danced round Kepa Arrizabalaga and tapped the ball into an empty net.

With Alexis Mac Allister and Moisés Caicedo outplaying Mateo Kovacic and Conor Gallagher in midfield, Brighton were dominant. Stewards had to restrain fans near the Chelsea dugout and the emotion got the better of De Zerbi, who marked the first home goal of his tenure by charging on to the pitch.

De Zerbi has joined a good, smart club. Brighton’s creative juices were flowing and they doubled their lead after more shambolic defending from Chelsea, Solly March’s corner flicking off Gallagher and Ruben Loftus-Cheek turning the ball into his own net in the 14th minute.

Potter had botched his tactics. De Zerbi had his team in a 4-2-3-1 system, with Adam Lallana scheming behind Trossard, and Brighton kept running beyond Pulisic and Sterling. The combinations between Estupinan and Mitouma were a threat on the left and March had the time of his life against Cucurella, who had a dire afternoon against his old team at left centre-back.

Yet there were reminders of Chelsea’s threat. Gallagher was denied by two brilliant saves by Robert Sanchez and Pulisic missed an open goal. It proved costly. Brighton pushed for a third and got it just before half-time. Again they broke through down the left, Caicedo releasing Estupiñán, whose cutback was diverted in by Trevoh Chalobah.

It was a disaster for Chelsea, who had to replace the injured Arrizabalaga with Édouard Mendy, and Potter made tweaks during the interval. The wing-back experiment was over, Loftus-Cheek moved to right-back and Chelsea had hope when Kai Havertz headed in Gallagher’s cross.

Yet for all that Chelsea pushed, with Pierre-Emerick Aubameyang coming on to extend Robert Sánchez, the comeback never materialised. Ultimately the occasion was summed up by the locals heckling Cucurella when the £62.5m defender went off in the 64th minute. Chelsea had been outplayed and the fourth goal arrived when Mendy pushed out a shot from the substitute, Julio Enciso, in stoppage time.

There was Pascal Gross, who had started the day at right-back, popping up on the left to score the rebound. Still smart and versatile, Brighton were not in a forgiving mood.