Zouma glanced in a close-range header just before half-time, but the Cherries were furious as the ball appeared to hit the hands of Hammers defender Thilo Kehrer earlier in the move.
However, after a check by the video assistant referee the goal was allowed to stand as they deemed the handball accidental and said it had not directly led to a goal.
Nevertheless, Bournemouth caretaker boss Gary O'Neil was upset with the decision and was booked after talking to referee David Coote as the teams left the field at half-time.
The hosts were awarded a penalty in the 91st minute when Bournemouth's Jordan Zemura was deemed to have handled the ball when sliding in trying to block a cross, with Said Benrahma converting from the spot to secure victory.
It was a tough evening for the Cherries, now without a win in three matches, as they lost striker Dominic Solanke and goalkeeper Neto to injury after only 45 minutes.
O'Neil later said: "We produced a really good second-half performance. It is so hard to find the positives now with all the emotions of the game but we did well. Hard to be be without our captain Lloyd Kelly and to then lose Dominic Solanke as well was disappointing.
"We responded well in the second half. There were bits to be proud of but of course we are in the results business and we don't want to come away to West Ham and lose.
On his discussion with the referee at full-time about West Ham's first goal, O'Neil continued: "We disagree. It's impossible for the goal to stand. Having your hands in front of your stomach, it pushes the ball into a different position. No different to JZ's [Jordan Zemura]. We seem to be getting the decisions go against us. 10 massive decisions have gone against us since we have been here.
"Jordan [Zemura] for the penalty, anyone who slides at that pace knows his hand will come up. I understand the penalty decision but it's hard for him to do anything else. It hits him on the hand and you think this is obviously going to be given.
"The first half was not good enough but the second half was better. To go six unbeaten with a newly promoted team is incredible. Still, credit to the boys for the start that we have made and that the results that are going against us have been unlucky decisions."
On Solanke and Neto's injuries, he concluded: "No idea how they are doing but hopefully nothing too serious and they are ok."