It was the third consecutive draw for Southampton.
West Ham had a good chance in the 68th when midfielder Jarrod Bowen fired from close range, producing a save over the bar by goalkeeper Alex McCarthy.
The Hammers will be without top-scorer Michail Antonio when they host Cristiano Ronaldo and Manchester United next weekend. The Jamaica international, who has four goals, was sent off moments before the final whistle after receiving his second yellow card for a dangerous challenge.
More AP soccer: https://apnews.com/hub/soccer and https://twitter.com/AP_Sports