Moura found the top corner from 25 yards after some impressive skill to open the scoring, with Davinson Sanchez and Son Heung-min adding further goals in the second half as Spurs made it four games without defeat in the league under the Italian.
That run has helped propel them back into the top-four race and they are now two points behind West Ham with a game in hand as the Conte effect begins to take hold in north London.
The obvious elephant in the room is Harry Kane’s lack of goals as the England captain has netted just once in 13 league games this season, and he again missed chances he would have expected to score.
Norwich, who remain bottom after Newcastle’s win on Saturday, will be wondering how they lost the game so heavily as they missed big chances at key moments, but Dean Smith will take heart from their performance.
One of those fell to Teemu Pukki in only the third minute and things might have been different had he scored.
Adam Idah got in down the right and pulled it back perfectly for the Finland striker, but his shot was straight at Hugo Lloris and Spurs survived.
That proved important as the hosts got a foothold in the game and former Canary Oliver Skipp reminded Norwich fans why they loved him so much last season, with a driving run through the middle of the pitch, but his shot was straight at Tim Krul.
Conte’s side found the breakthrough in the 10th minute with a goal of real quality.
After a nice piece of skill to round a Norwich defender, Moura then played a one-two with Son, turned his marker and thundered an unstoppable drive into the top corner.
That gave Spurs a solid base to build on but they could not find the quality to add to their scoreline.
Ben Davies might have converted at the far post after Son’s free-kick made it all the way through, while Kane inadvertently diverted Son’s shot wide.
Kane’s frustration in front of goal was growing as he missed another chance before the interval. Moura’s ball set him free and he spotted Krul off his line, but his chip from 30 yards was wide of the target.
Norwich were very much in the game and should have equalised after a dominant start to the second half. Brandon Williams got in down the left and pulled the ball back to Pukki, whose skewed shot fell straight to Idah, only for the Irishman to divert it wide from a golden position.
As is usual in the Premier League, the Canaries were made to pay as Tottenham doubled their lead in the 67th minute.
Kane’s quest to end his drought was thwarted again as Krul did brilliantly to claw away a low shot that looked destined for the bottom corner, but from the resulting corner, Sanchez smashed in a loose ball from close range.
It was 3-0 10 minutes later as Davies played a one-two with Skipp before teeing up Son, who fired into the bottom corner.
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