The match looked to be heading for a stalemate until Huddersfield conceded their first league goal of the campaign in unfortunate fashion in the 72nd minute.
Pedro Obiang’s shot hit Mathias Jorgensen on the back and looped agonisingly over the stranded Jonas Lossl and in off a post.
Substitute Andre Ayew then poked home following a corner five minutes later to ease the tension around the London Stadium.
“I am happy for the lads, I am happy for the whole club,” Bilic told Sky Sports. “It was very important for us.
“We started with three away games, three defeats. It was a must-win game. I was pleased with the way we played. Even if we didn’t win the game I could say nothing to the lads, they gave everything.
“We played good. It wasn’t a nice performance but it was a top performance in all other stuff, in the second balls, in determination, in closing them down, in getting the corners and free-kicks and all that. We totally deserved it.
“I’ve felt the pressure for a whole year now, it didn’t start today. Although for me it’s not logical to be under pressure after three games only but it is modern football and of course I have felt the pressure.
“But we kept the calmness, we changed a little bit the shape of the team and we said to the guys that you’re going to go back to basics.
“It’s all about confidence. We have a quality team with quality players, some players are still missing but we have to keep the clean sheets to stop them from having the ball in dangerous areas to hurt us.”
Huddersfield boss David Wagner had no complaints with the result despite the unfortunate nature of the opener as his team lost for the first time this season.
“We were not good enough,” he said. “It was a deserved result, we were second best more or less in every area. Maybe the second half was slightly better.
“Our biggest problem was with the ball, I think we worked, we fought, we tried to keep the ball out of the goal but with the ball we were not good enough. We lost the ball too easy, we were never able to keep the ball.
“I’m unsure if we were nervous, today we looked like a promotion team with some nerves.
“It makes no sense to play football without bravery and without liking to have the ball and to be comfortable on the ball.
“You have to be brave to play with the best. Today we have seen what happens if we are not brave enough.”