Wes Hoolahan opened the scoring and Grant Holt, from the penalty spot, and Aaron Wilbraham put Lambert`s side in control before the Foxes pulled a goal back in injury time.
"That's as good as we have been this season. We dominated from start to finish away from home and in front of a vibrant crowd. We thoroughly deserved to win," said Lambert.
And Lambert insisted Norwich had the pedigree to maintain their promotion push, adding: "We have surpassed what we thought we could do. The three-year plan was to survive in this league. Now we have as good chance as any - QPR, Cardiff, Leeds and Swansea - of going up."
The Norwich manager also saluted goalscoring midfielder Hoolahan.
He said: "Hoolahan was unplayable. Leicester could not get near him. His performance was outstanding. It was right up there with the best he had produced."
Source: PA
Source: PA