The Brazilian opened the scoring with a thunderbolt in the 10th minute at the Tottenham Hotspur Stadium.
Second-half strikes from Davinson Sanchez and Son Heung-min sealed the victory as Antonio Conte's side leapfrogged Arsenal into fifth in the Premier League table.
Spurs are unbeaten in four Premier League games under Conte and trail fourth-placed West Ham by two points in the race for Champions League football. Norwich remains bottom following its first defeat under Dean Smith.
Unbeaten in four Premier League games, the Canaries had the first chance inside three minutes; Teemu Pukki drawing a smart save out of Hugo Lloris from point-blank range.
But the host took the lead in emphatic fashion seven minutes later. Lucas skipped away from a couple of challenges and played a neat one-two with Son, before drilling a stunning 25-yard effort into the top corner.
Despite losing Sergio Reguilon to injury, Spurs went close to adding a second before half-time.
Ben Davies was just unable to turn the ball home from a free-kick, while Harry Kane's ambitious chip from distance was not too far wide.
Looking to win consecutive Premier League games in London for the first time since 1992, Norwich squandered a great opportunity to equalise just before the hour mark.
Brandon Williams cut the ball back for Pukki, whose mishit shot was deflected wide from close range by Adam Idah.
It proved costly as Spurs doubled their lead in the 66th minute when Sanchez lashed home after Son's corner ricocheted kindly into his path.
Son then got in on the act as he put the icing on the cake 13 minutes from time. Receiving the ball from Davies in the box, the South Korea international skipped away from a challenge and fired beyond Krul and into the bottom-left corner.