The Hammers returned to winning ways in the Premier League with a 2-1 victory over the Saints at the Boleyn Ground in London.
Southampton took the lead after just 13 minutes when Arsenal-owned defender Carl Jenkinson scored an own goal.
Michail Antonio made it 1-1 in the 69th minute, and 10 minutes later Andy Carroll won the game for the Hammers.
Carroll came on a substitute for Mauro Zarate at half time, while Manuel Lanzini also replaced Alex Song at the start of the second period.
West Ham co-chairman Gold was impressed with the changes Bilic made against Southampton and has written on the club’s official website: “The decision by the manager to change things at half-time was both brave and decisive.
“I take my hat off to Slaven as I thought his timings of the substitutions and the switching of the full-backs made the difference.”
West Ham will return to action on Saturday afternoon when they face Liverpool at home in the Premier League.
The London outfit are eighth in the standings at the moment with 29 points from 19 matches, six points behind Tottenham Hotspur, who are currently fourth and occupy the final Champions League spot.