Daniel Farke's side needs just five points from its remaining six games to be certain of an immediate return to the top-flight after last season's relegation.
The Canaries could go up as early as Sunday (AEST) if they win at Derby and other results go their way.
Norwich scored five first-half goals at Carrow Road, with Pukki netting twice, and Emi Buendia, Todd Cantwell and Kieran Dowell also on target.
Finland striker Pukki went on to complete his treble with a second-half penalty before substitute Jordan Hugill completed the rout.
Norwich's biggest win of the season lifted it eight points clear of second-placed Watford and 17 ahead of third-placed Brentford.
The teams who finish first and second in the Championship are promoted automatically, with the next four clubs going into the play-offs.
Brentford's faltering promotion push suffered another setback as Birmingham boosted its survival hopes with a 0-0 draw in west London.
Thomas Frank's side squandered a string of clear-cut chances, with poor finishing and some fine saves from Neil Etheridge putting a big dent in their bid for a top two finish.
Brentford is nine points behind Watford with a game in hand, while Birmingham moved seven points clear of the relegation zone.