Goalkeeper John Ruddy tipped a shot from Albion's Peter Odemwingie on to the bar and Canaries midfielder Andrew Surman then cleared James Morrison's drive off the line before volleying the 43rd minute opener which handed the visitors the advantage.
The Baggies continued to press after the break and Shane Long came off the bench to equalise with a penalty in the 68th following Daniel Ayala's foul on Jerome Thomas - but a breakaway at the other end 11 minutes from time saw Steve Morison nod in the winner from a Grant Holt cross.
It was a second consecutive away win for Norwich, who remain ninth in the table, and Lambert said: "It was an absolutely fantastic result.
"I thought the lads were excellent. They defended really strongly when they had to and counter-attacked really quickly, which was great.
"With the first goal Wes Hoolahan plays in the cross and it still has to be finished, which Surman does perfectly well.
"For the second, Holt does fantastically for us and then what a header from Morison, because he has to get above a defender and beat the goalkeeper.
"I am absolutely delighted. The lads put their bodies on the line and Ruddy was on top of his game - great credit to the lads for the way they defended."
The Canaries - promoted to the top-flight last summer just a year after they gained entry to the Championship by winning the League One title - were tipped by many in pre-season to struggle this term, but they now have an impressive total of 28 points from 21 Premier League games.
The progress of Lambert's side shows little sign of slowing, although the Scot is adamant he is not about to start looking up the table rather than down.
"I'm pretty sure everyone thought we would be in the bottom three at this point," Lambert said.
"We came up from League One really quick, so to be ninth is terrific for this team.
"I never look upward, I just concentrate on us and where we are going to finish. We will see."
The result was 15th-placed West Brom's third defeat in a row in the league and leaves them five points above the relegation zone.
Albion boss Roy Hodgson felt the outcome was harsh on his team but admits the Baggies need to turn things around quickly.
"I thought the way we equalised was a just reward for the effort that we that made, but then we got caught on another counter-attack and Norwich were able to hang on for the victory," Hodgson said.
"I'm sure with their organisation and determination, their manager feels they deserved it, but for us, it feels a bit harsh.
"There was a ball cleared off the line and their goalkeeper made a couple of good saves, whereas ours wasn't really involved too much.
"But that's football - we have to get over it, deal with it and try to get ourselves back into winning ways, in particular at The Hawthorns."