The visitors won their third straight league game with a second-minute goal from Dele Alli, followed by a double from Harry Kane, including one from the penalty spot at Carrow Road.
Tottenham and Arsenal both have 45 points but Spurs has the better goal difference. Arsenal and Southampton drew 0-0 Tuesday.
Tottenham, which recorded its fifth straight victory in all competitions, is shaping up as a serious contender for its first league title since 1961. But Norwich, with four league defeats in as many matches, is only two points above the relegation zone.
The Canaries were back in action for the first time since their 5-4 defeat against Liverpool.
There were only 96 seconds gone when Alli gave Tottenham the lead. Christian Eriksen's shot was well saved by Declan Rudd, but Alli was quickest to the rebound to open the scoring.
Tottenham made it 2-0 after 30 minutes with both Alli and Kane involved. Kane's fierce shot stung the hands of Rudd before Alli was adjudged to have been fouled by Sebastien Bassong in the penalty area, and Kane sent Rudd the wrong way.
Alli was substituted at halftime - reportedly through illness, rather than injury - and Norwich enjoyed the best of the second period.
But Spurs scored the only goal of the second half when Kane, who moments earlier had hit the post, scored his 14th league goal from his last 15 appearances with a cool finish after Martin Olsson was dispossessed by Eriksen.
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