Goal from Morgan Gibbs-White and Nikola Milenkovic gave the visitors a comfortable lead before Jarrod Bowen’s wondergoal made things tense in the final few minutes.
After over ten minutes added time and plenty of theatrics from the Nottingham Forest players, the final whistle blew, and they remain in contention for Champions League qualification.
Forest currently sit in seventh with 65 points, one behind fourth-placed Chelsea who they play in their final game of the season.
Speaking to the press after the game, Espirito Santo admitted he was a little anxious, saying: "Until then (West Ham goal) we were in control. Then the anxiety comes when we allowed the goal and everything is difficult from there. Matz )Sels) did great again so we're happy.
"We started really well. Previous games a lot of bad things happened to us but today was not the case. Today we pressed good, got a good goal, started well in the second half, on the front foot. Generally a good performance.
"The players worked hard to put West Ham under pressure."