The Hornets decided to rest new-boy Ismaila Sarr but fellow recent arrival Craig Dawson got the nod. Potter selected a back three in his first game in charge and the Seagulls were on the back foot early on, struggling to play out and attracting pressure.
There was an early worry for the hosts as Troy Deeney inadvertently caught strike partner Andre Gray in the eye, but the forward recovered and carried on.
Brighton eventually grew into the game and took the lead on 28 minutes. After Glenn Murray had clipped wide, they followed up as a ball to the back post was squared by Pascal Gross, only to be diverted into his own net by Abdoulaye Doucoure.
The hosts could not find a response before the break and were again second best once they returned, but should have been level although Gray could not convert a cutback.
That seemed to give Javi Gracia's side some encouragement and they had a penalty turned down by VAR when Roberto Pereyra's free-kick was blocked by Murray. The Argentine protested that the veteran had used his arm, but the men in the booth decided it was not enough to call a penalty.
However, just as the hosts seemed to be taking over, Brighton produced a sucker punch when, with his first touch off the bench, Florin Andone whipped home past Ben Foster at the near post just 40 seconds after coming on.
Andone was introduced at the same time as new signing Neal Maupay and, having netted 28 goals for Brentford last term, the Frenchman displayed fantastic composure to round the goalkeeper and slot home for 3-0.