Ward-Prowse gave West Ham the lead in the 19th minute as he fired home from close range after good work down the wing from Antonio.
Antonio was too strong for Brighton defender Adam Webster and picked out England international Ward-Prowse, who recently joined from Southampton, to tap in from two yards.
Manager Roberto Di Zerbi stuck to his promise of handing a first Premier League start of the season to Republic of Ireland striker Evan Ferguson.
And he missed a good chance to cancel out Ward-Prowse’s opener when he failed to convert a header.
Bowen added a second for David Moyes’ side 13 minutes into the second half, expertly controlling Said Benrahma’s cross before firing into the bottom corner.
The 31 successful passes West Ham managed was the lowest of any top-flight team since 2006 – when Watford had one fewer against Portsmouth
Despite having more possession, Brighton struggled to contain West Ham’s fluid counter-attacks and Bowen teed-up Antonio to seal the points.
Antonio drilled a shot into the corner after 63 minutes to send the travelling fans into raptures.
Brighton, who enjoyed 79 per cent of possession, pulled a goal back with nine minutes to play when German midfielder Pascal Gross chopped back onto his right foot to drill through a crowded penalty area.
It was the German’s 27th goal for Brighton, putting him ahead of Glenn Murray as the club’s top Premier League goalscorer.
The hosts threatened to set up a grandstand finish as Alphonse Areola made two crucial saves in the dying stages.
Firstly, the Hammers goalkeeper brilliantly kept out Joel Veltman’s volley, before Ferguson’s fierce drive was tipped over by the Frenchman.
The saves justified Moyes’ decision to make Areola his number one this season.
Brighton also had a strong appeal for a penalty turned down after the ball appeared to strike West Ham right-back Vladimir Coufal’s arm in the box.
The Seagulls were condemned to a first defeat of the season and was the first time they had lost to the Hammers in 13 league matches.