Villa won 2-1 with goals from Christian Benteke and Charles N'Zogbia, while an Ashley Westwood own goal was all West Ham had to show for their day in the Midlands.
This was Villa's first win in nine league games and Lambert was delighted.
He said: "It's only great when you hear the whistle and you've won. It's the only good thing about it. The stress levels are ridiculous.
"It's hard to explain. You have to be in that position. Balls are going into your box. But once it's finished it's great you have won.
"It's a huge win for us. We have been in positions of being goals up in a right few games.
"If we had taken more points from those, we'd be comfortably in mid-table.
"But the pleasing thing is we have hopefully broken the camel's back with that."
All the goals came late in the match. Benteke scored the opener from the penalty spot after 74 minutes before a stunning free-kick from N'Zogbia put them in control four minutes later.
The Scot added: "N'Zogbia's goal was world-class. He's got that in him. He's a really talented footballer.
"To be fair, over the last couple of months, Charles has been excellent. He was unlucky because he had a bad injury.
"That kept him out for six weeks or so.
"Since he's come back into the fold he's been excellent. He has been very good."