The visitors took the lead after just four minutes thanks to a goal from Jacob Murphy, and it was starting to look like the same old story for West Ham.
Star man Lucas Paqueta restored parity in the 35th minute before an own goal from Sven Botman gave West Ham the lead going into the break.
Thomas Soucek scored their third in added time, earning Espirito Santo his first win since replacing Grah Potter in September.
Speaking to reporters after the game, the Portuguese boss was full of praise for the home supporters.
“I think we mentioned in the press conference,” he said. “Our idea is to try and give something to our fans and today we did give them a small thing and the way they gave us back was huge.
“In the end, the noise in the London Stadium was amazing, so we cannot thank them enough. Let’s try against Burnley to give them a little bit more so they can make more noise as we try to transform the London Stadium into a very hard place for our opponents.”