The Canaries now need just five points from their remaining six fixtures to be certain of promotion, and could go up as early as Saturday if they win at Derby and other results go their way.
Norwich scored five first-half goals to leave the Terriers reeling, with Pukki netting twice, and Emi Buendia, Todd Cantwell and Kieran Dowell also on target.
Pukki went on to complete his treble, making it 25 goals for the season, with a second-half penalty before substitute Jordan Hugill completed the rout.
It was an evening to forget for Huddersfield’s stand-in keeper Joel Pereira, who was called into the side at the last minute after Ryan Schofield felt ill in the warm-up.
It was only the Portuguese’s second appearance for the club and he was left horribly exposed by those in front of him as Norwich romped to their biggest win of the season.
They took the lead after just eight minutes as Cantwell picked up a loose ball just outside the box and made his way along the byline before squaring for Pukki to tap into an unguarded net from close range.
The rampant Canaries made it 2-0 in the 20th minute with Pukki firing high into the net after being picked out by a sublime through ball from deep by Buendia - and two more quick goals doubled the hosts’ advantage before the half hour mark.
Buendia’s crisp strike from just outside the box that went in off the upright stretched their advantage and then a scintillating move, with Buendia again in the thick of things, ended with Cantwell slamming the ball home.
It was breathless stuff, with Buendia also hitting the crossbar after Kenny McLean had touched a free-kick to him.
Norwich netted a fifth three minutes before the break when Buendia played a slick one-two with Dowell and then had the vision to find his midfield colleague again for the simplest of finishes.
Norwich looked hungry for more goals after the break and duly made it six just past the hour mark.
Referee Jarred Gillett pointed to the spot when Oliver Skipp went tumbling in the box under a challenge from Isaac Mbenza and Pukki sent Pereira the wrong way with a perfectly struck penalty.
Huddersfield almost grabbed a consolation in the 72nd minute, with Tim Krul making an excellent block to deny Danny Ward after Demeaco Duhaney’s header had come back off the upright.
But it soon got even worse for the Yorkshire side as City made it 7-0 after 78 minutes, Max Aarons crossing from the right for Hugill to sweep home moments after he had come off the bench.