West Ham have now lost five of their opening six Premier League games after Austin, Tadic and Ward-Prowse sealed a 3-0 win for Southampton.
Southampton tore through a sorry West Ham defence to rack up a 3-0 win at London Stadium on Sunday and pile more misery on an embattled Slaven Bilic.
Charlie Austin, Dusan Tadic and James Ward-Prowse got the goals to seal a fourth win in a row in all competitions for Claude Puel's side, who have kept clean sheets in all of those successes.
By some contrast, West Ham have now shipped 14 goals in four Premier League games, despite the hosts siting deep and allowing Southampton the ball in a bid to avoid the sort of first-half collapse they suffered at West Brom last week.