Hubertz scored the opener two minutes before the break before crossing for Andy Holt to head the second in the 62nd minute.
Kirk made sure of the points with a clinical strike after latching on to an Alex Russell pass three minutes later.
It was Huddersfield's fourth defeat on the trot in league and cup and manager Andy Ritchie pointed at a sickness bug which had laid low some of his players over the last few days.
He said: "We had five or six lads being sick at half-time and, while I am not using that as an excuse, it hasn't helped."
Whatever the reason, Northampton were in the driving seat throughout and should have been ahead before Hubertz rose at the near post to convert a Bradley Johnson corner with half-time looming.
Johnson had been guilty of the worst miss in the 28th minute when he fired wide from a matter of yards with the goal gaping at his mercy.
None of this mattered as the Cobblers stepped up the heat after half-time with firstly Hubertz setting up Holt and then Kirk ramming home his fifth goal of the season.
It could have been worse for the Terriers as their substitute Frank Sinclair narrowly avoided heading an Alex Russell free-kick past his own goalkeeper, while Hubertz had two other fierce efforts either saved or deflected wide.
It was a sorry afternoon for Huddersfield who took until the 90th minute to test home goalkeeper Mark Bunn with skipper Andy Booth's snap-shot well saved by the goalkeeper.