The game appeared to be heading for a goalless draw - leaving both sides without maximum points heading into the international break - but Adama Traore struck in the third minute of added-on time to secure success for the West Midlands outfit.
Wolves have moved into ninth place in the standings, while West Ham remain at the bottom having lost each of their opening four matches of the top-flight campaign.
However, it was Wolves who soon made their mark on the game and kept West Ham on the back foot, with Joao Moutinho firing wide from outside of the area and Matt Doherty bringing a smart save out of Lukasz Fabianski.
West Ham came back into the contest as the game progressed past the half-hour mark, with Robert Snodgrass sending a shot into the side-netting, but Wolves could have taken the lead when Moutinho's cross was headed over by Diogo Jota.
Raul Jimenez also fired marginally wide for Wolves just before the break, but West Ham were able to remain on level terms despite being second best for much of the opening 45 minutes.
Conor Coady kept Wolves on level terms with a block in front of goal with less than 20 minutes left while down the other end, Fabianski did well to prevent Leo Bonatini from netting for the second successive game in all competitions.
Both teams continued to create chances, with Raul Jimenez failing to convert from close range after the ball got stuck between his feet and Marko Arnautovic being denied by an advancing Patricio.
A point would have probably been a fair result but deep into additional time, Bonatini teed up Traore to fire the ball into the corner to give the newly-promoted side their first league triumph since earning a return to the top flight.
WEST HAM UNITED (4-2-3-1) Fabianski; Fredericks, Balbuena, Diop, Cresswell; Sanchez, Wilshere (Obiang 64'); Antonio (Hernandez 75'), Anderson, Snodgrass (Yarmolenko 46'); Arnautovic
WOLVERHAMPTON WANDERERS (3-4-3) Patricio; Bennett, Coady, Boly; Doherty, Neves, Moutinho, Jonny; Jota (Traore 62'), Costa (Bonatini 72'), Jimenez (Vinagre 87')