The Hammers went into the game having won their last two games in a row, with 2-1 and 2-0 victories over Southampton and Liverpool respectively, whilst Wolves had also enjoyed an upturn in form, winning their three previous fixtures in the Championship.
This was a meeting between two in-form teams, but for most of the game, it looked like they would play out a 0-0 stalemate.
Wolves only enjoyed 43% of possession and mustered only two shots on goal, with West Ham knocking on the door for a winner until it finally came in the 85th minute.
Striker Nikica Jelavic was handed a rare start, and he was the match-winner as he beat Carl Ikeme with a fine half volley in the dying embers of the game.
West Ham now advance into the fourth round of the competition, whilst Wolves will return to Championship action in with a home game against Fulham.