Summer signing James Ward-Prowse scored his first Hammers goal in only his second start to set the visitors on course for a first ever Premier League win over the south coast side.
Manager Moyes said: “I’m thrilled with the three points because usually we come here and struggle to get any points.
“We haven’t won here for years. It’s been the same coming here and not getting the results.
“Today was a well-deserved three points. Brighton did a good job, but we also did a good job in other parts of the game.
“Brighton have got an extremely good manager and his side are causing problems to plenty of teams, not just us.
“They are going to be hard for any manager to play against.
“They are very offensive, which is great, but that also means it can open up and give you chances on the counter.
“We worked hard on not getting picked off easily and we defended really well.
“Our counter-attacks were really good. Two or three years ago we were really good on the counter and we showed that. All the forward players made a really good contribution today.”
Moyes led West Ham to their first trophy in more than 40 years by winning last season’s Europa Conference League.
On their surprise early-season surge to the Premier League summit, the Scot said: “I didn’t realise we had gone top. It has been a long time since any West Ham manager did that also.”
Ward-Prowse got West Ham off to the perfect start when he opened the scoring after 19 minutes, following on from his two assists in last weekend’s debut win over Chelsea.
Jarrod Bowen added a second 13 minutes into the second half – expertly controlling Said Benrahma’s cross before firing into the bottom corner.
Bowen then teed up Antonio to seal the points in the 63rd minute with a drilled shot into the corner.
Brighton, who had 79 per cent of the possession, got a goal back with nine minutes to play when German midfielder Pascal Gross chopped back onto his right foot to rifle home through a crowded penalty area.
Brighton manager Roberto De Zerbi said: “I’m disappointed with the result. It wasn’t the best performance in my time at the club, but we didn’t play badly.
“We shot 27 times and created 11 chances to score. In the second half I’m disappointed because we lost the balance of the game.
“I’m very proud of the performance, the attitude, the passion and the mentality to play well and get points.
“I can analyse how we conceded the goals and how we made a lot of mistakes in the last 20 metres and how we conceded so many counter-attacks, but it is not a problem.
“We will start on Monday working on the last week.”