JWard-Prowse opened the scoring with his first Hammers goal when he tapped in from two yards out in the 19th minute after good work from Michail Antonio.
Jarrod Bowen added a second for the visitors in the 58th minute, bringing down Said Benrahma's cross before poking the ball into the corner.
And though Brighton continually dominated possession and territory, Bowen set up Antonio to drill a shot into the corner for the away side's third in the 63rd minute.
The Seagulls scored a late consolation goal when Pascal Gross' drive effort found the far corner, but David Moyes' men survived a late surge of Brighton pressure to go on to victory.
"A lot of effort went in to the game plan, you have to respect Brighton," Ward-Prowse told BBC Match of the Day.
"We denied Brighton space and were compact and clinical. We had the composure to make the most of our chances when we had them - we executed our game plan perfectly."
Ward-Prowse praises 'fantastic' West Ham
West Ham have made an excellent start, backing up their win over Chelsea last weekend with a ruthless display in Sussex.
Incredibly, the visitors' 31 successful passes in the first half was the lowest total reached by a Premier League side since November 2006, when Watford had 30 against Portsmouth.
But they still went ahead through Ward-Prowse, who bundled Antonio's cross over the line after Adam Webster was caught in possession.
It was Ward-Prowse's third goal involvement in just his second game for the Hammers having joined from boyhood club Southampton this summer for around £30m.
"It's been fantastic. I can't speak highly enough of the fans and the people that have helped me settle," the England midfielder added.
As Brighton pushed after the restart West Ham exploited the space their players left behind, and Bowen brilliantly controlled Benrahma's cross-field ball in a counter-attack before finding the bottom corner.
Five minutes later the three points were wrapped up thanks to Antonio's fine finish after creating space for himself. The Jamaica international almost added a fourth in the closing stages but prodded a shot over when through on goal.
Ward-Prowse also had a chance to add a fourth late on, but his shot from a tight-angle was saved before the rebound off a Brighton defender hit the cross bar.
"Today was a well-deserved three points," Moyes told BBC Match of the Day. "All the forward players had a really good contribution."
Brighton lack ruthless touch
Brighton finished the match with 79% of possession but, despite scoring four goals in each of their last two matches, initially struggled to trouble West Ham keeper Alphonse Areola.
"It can happen in football. I am really frustrated for the result but not for the performance," said Brighton boss Roberto De Zerbi to BBC Match of the Day.
"We made some crucial and important mistakes for the first and third goals. We could be more clinical but when you concede the first goal, the space becomes smaller and it is more difficult."
Brighton's best chance at finding a way back into the game came just after the restart when Areola dived to his left to keep out an Evan Ferguson header with Brighton one goal down.
The Seagulls rallied after going three down and scored in the 81st minute as Gross' driven shot from the edge of the box found the bottom corner.
That sparked a flurry of chances for De Zerbi's men, with Joel Veltman's volley forcing a fine save from Areola and the hosts having a penalty shout turned down after the ball was deemed to have accidentally struck West Ham's Vladimir Coufal's arm in the box.
In injury time Ferguson blasted a fierce shot which was only just tipped on to the bar by Areola, but by that stage defeat was inevitable and Brighton fell to their first loss to West Ham in 13 Premier League matches.