Brighton, who had topped the table after two 4-1 wins in their opening two games, dominated possession and registered 26 attempts on goal, but West Ham made the most of what little possession they had to grab the win.
Antonio had the game’s first effort on target in the sixth minute as he latched on to a perfect angled pass from Lucas Paqueta, but his shot lacked power and was easily saved by keeper Bart Verbruggen, who was making his debut for Brighton.
The new keeper only managed to keep his clean sheet intact for 19 minutes as Antonio forced Adam Webster into a poor back-pass before feeding the ball to Ward-Prowse, who bundled it home at the second attempt. The goal was his first since arriving from Southampton in August and his 50th overall in the Premier League.
Bowen added the second in the 58th minute, controlling a brilliant cross-field pass from Said Benrahma before swiftly tucking the ball home at the foot of the far post.
Excelling in the lone striker role, Antonio rifled home a low drive to make it 3-0 five minutes later, but Pascal Gross drilled a low shot into the far corner to make it 3-1 in the 81st minute to throw Brighton a lifeline.
Brighton had plenty of chances late on, but keeper Alphonse Areola pulled off some superb saves as the Hammers held on to record their first Premier League win over the Seagulls at the 13th attempt.
West Ham are level with Tottenham and Arsenal on seven points and top the standings on goals scored. Brighton slipped to fourth on six points.
