Goals from Christian Benteke and Charles N'Zogbia put Villa in control and all West Ham could manage in reply was an Ashley Westwood own goal as the home side held on for a 2-1 triumph.
It was Villa's first win in nine league games after collecting only three points from the previous 24 available.
Lambert admitted: "It's only great when you hear that 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. You just have to see it through.
"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.
Lambert said: "The free-kick was world-class, an absolute world-class goal. 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 with his knee. 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.
"He's got that X-Factor. These type of players are not easy to come by."