Brighton narrowly avoided relegation last term under Chris Hughton but, with Potter now at the helm, put that misery behind them as Abdoulaye Doucoure’s first-half own goal gave them the lead.
The Seagulls had travelled to Vicarage Road on the opening day of last season, losing 2-0 on that occasion, but the scoreline was reversed as substitute Florin Andone, with virtually his first touch of the game, doubled their lead.
Just minutes later, Neal Maupay, who signed for the Seagulls on Monday, justified his £20m price tag with a debut goal, calmly finishing after rounding Watford goalkeeper Ben Foster.
“To score three away from home and not concede is a dream,” Potter told BBC Sport.
“The preparation was first class. Overall I thought we tried to do what we set out to do and then you just need a bit of luck and quality.
“We’ve worked hard every day. There is a really good foundation from what has been done previously – our job is to get better. You can see how they have applied themselves, now we dust ourselves down and don’t get carried away.”
Watford, who finished 11th in the league last season and reached the FA Cup final, made the more promising start but their late slump at the end of 2018-19, in which they lost their final three matches of the campaign, continued into the new season.
Not since the opening day of the 2015-16 term – when they were in the Championship – had Brighton won their first league match of a season.
“What I know is that they played better than us and deserve the victory today. No excuses. It is the first game and we try to improve for the next one,” said Watford boss Javi Gracia.
“The best news is that it is the first game. Sometimes it is good to wake up and improve – we need to do that for the next game.
“There were many individual mistakes. The first and second goal, they took advantage. We expected them to play three at the back and with that shape. We worked in the week to adjust well, but [did so] after they got the win.”
Brighton finished 17th in the Premier League last season but a new campaign marks a fresh start for the Seagulls with Potter at the helm.
Managing his first Premier League match since replacing Chris Hughton in May, new signings Maupay, Leandro Trossard, Adam Webster and Aaron Mooy all started on the bench.
After a shaky start, the Seagulls soon settled at Vicarage Road, but little separated the two sides until Watford’s Doucoure turned a Pascal Gross cross – destined for the boot of Glenn Murray – into his own net.
It marked the first time the away team had scored – albeit in this case with a helping hand – in a Premier League meeting between Watford and Brighton.
Half-time soon arrived but although it was the hosts who looked the more likely to score after the break, they were undone when Romania international Andone tapped in Davy Propper’s cross from close range, moments after being introduced.
Victory was sealed just minutes later as Maupay latched onto a through ball, his goal confirmed after the video assistant referee – making its Premier League debut this season – checked for a possible offside.
