West Ham defender Nayef Aguerd proved the matchwinner against Southampton on Sunday.
The result leaves Southampton bottom of the table.
Aguerd headed home Thilo Kehrer's free-kick but had to wait more than three minutes to celebrate after a lengthy check by VAR.
West Ham forward Jarrod Bowen hit the crossbar, while Southampton centre-forward Paul Onuachu headed against the bar late on.
The win sees West Ham mve out of the relegation zone and up to 14th.