Saints twice equalised, with Jay Rodriguez and Pablo Osvaldo cancelling out efforts from Gabby Agbonlahor and Libor Kozak.
But Villa would not be denied as Delph scored a fabulous winner with
ten minutes remaining to help Villa extend their unbeaten run to five matches.
"I thought we were outstanding the whole game," Lambert told Sky Sports.
"I thought his (Delph's) game was fabulous, I really did. He's been terrific for me this season, but the strike was just worthy of winning any game.
"I've nothing but praise for the team who came back really strongly in the second half and won a really good game."
When asked whether striker Christian Benteke will have benefited from not starting the game after seven scoreless matches, the Scot added: "I don't think the game is all about Christian Benteke. The game's about everybody who has gone out and scored.
"I think it was justified that we started the game with Gabby (Agbonlahor) and the game's not all about Christian.
"He's only a young lad as I said before. But to be fair, when he came on he showed what he can do."