Slaven Bilic admitted he was already preparing for a replay when Nikica Jelavic’s late strike sank stubborn Wolves in the FA Cup.
There were just five minutes remaining when former Everton striker Jelavic broke the deadlock, sweeping in a superb volley for his first goal for the Hammers.
Substitute Andy Carroll held the ball up on the edge of the box before feeding the Croat, whose first-time shot flew across Wolves keeper Carl Ikeme and into the net to secure a 1-0 win.
West Ham had dominated the previous 85 minutes but without creating a clear-cut chance against a miserly Wolves defence who had not conceded in their previous three matches.
The match will not live long in the memory but all that mattered to Bilic was a place in the fourth round of a competition he is eager to do well in.
“First of all it’s an FA Cup game, and they are very often tough even when you play against teams from two or three levels below,” said the Upton Park boss.
“I lost a game here as a player against Wrexham. So it’s well done to the lads, they played against a team which won their last three games without conceding.
“They were very stubborn, resilient, and it’s the same old story to unlock it; it has to be their mistake, or a shot from outside the box, or some extra quality.
“But we were patient, we kept our shape and (substitute) Andy (Carroll) as usual had a big impact and helped Jelavic score a wonderful goal. It’s good to go through with a clean sheet and a great goal.
“We were getting ready for a replay but the guys did everything to try to score. They pushed and pushed, it wasn’t the Alamo but if one team was trying to win it in one game it was us and we got our reward.
“I don’t think there will be any complaints from their side.”
Wolves were without their top scorer Benik Afobe after the club agreed a fee with Bournemouth for the 10-goal striker.
Yet they almost did secure a replay in injury time, only for substitute Adam Le Fondre to scuff his shot wide.
“That was probably our best chance of the game,” admitted Wanderers boss Kenny Jackett.
“It was a spirited performance, very resolute. We were working hard to take the game to West Ham but we couldn’t get the goal.
“It cost us in the end as they had one clear-cut chance and they took it.”
Jackett is waiting for an update on the condition of striker Bjorn Sigurdarson, who fell to the ground with no other player around him and was given lengthy treatment before departing the field on a stretcher.
“He just collapsed, there was no one near him. It’s his back,” added Jackett. “We hope he is okay.”