Lambert claimed the first on 16 minutes as he powered above the away defence to convert Puncheon's clinical cross for his 27th goal of the season.
The lead was doubled by strike-partner Barnard on 24 minutes when he met Hammond's clipped centre for his fifth goal in the last four games as the home side began to run riot.
The scoring continued via the impressive Puncheon who cut in from the left-hand side and curled a fine effort around Alex Smithies 10 minutes later. Huddersfield kept the score to three up until the 76th minute when Hammond was rewarded for a tireless display by connecting with Puncheon's corner for his fifth goal of the season.
Waigo emerged from the bench to fire Saints to their biggest win of the season as he round Smithies and then swiped the ball into an empty net on the turn in the 84th minute.