The Scotland winger ran onto a lovely diagonal ball from Bradley Johnson before controlling and then sliding home past Hugo Lloris in the 47th minute to give the Canaries the advantage.
The home side then managed to maintain their ascendency until the final whistle, pushing them four points clear of the relegation zone, and giving manager Chris Hughton some room to breathe.
After the match, the Snodgrass spoke of the importance of the victory which came courtesy of a much-needed clean sheet.
"Every one of the boys were terrific," Snodgrass said on Sky Sports 1HD. "The performances in the past three to four weeks have been terrific.
"All the lads have been scratching our heads because we've been shooting ourselves in the foot with silly goals we've conceded."
And in regards to chief executive David McNally’s recent comments regarding the apparent lack of job security for Hughton, Snodgrass added: "He's got a job to do. The points are what he wants. He wants points on the board and we haven't done that.
"I'm delighted, it's a massive three points today."
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