The 3-1 success at the John Smith's Stadium marked the first time since April 2017 that Saints have won back-to-back Premier League games and they pulled three points clear of the bottom three.
Philip Billing pulled one back for Huddersfield in the 58th minute – just the fourth goal the Terriers have scored at home in the league this season – but 18-year-old Michael Obafemi's first senior goal condemned them to a fifth straight defeat.
Hasenhuttl unsurprisingly stuck with the same side who beat the Gunners while David Wagner recalled Steve Mounie from suspension in attack but Huddersfield's struggles were rather summed by the fact neither he nor the man he replaced, Laurent Depoitre, has scored a goal this season.
The first half did not make pretty viewing for the home fans and Huddersfield's players headed down the tunnel with boos ringing in their ears.
They had nearly 60 per cent possession but did not manage an effort on target and it was only in stoppage time, when Mounie turned and shot over the bar, that they even came close to fashioning a decent chance.
Saints, on the other hand, broke with pace and purpose and fully merited their two-goal advantage.
Jonas Lossl got away with an early spill from Matt Targett's cross but could do nothing in the 15th minute when Pierre-Emile Hojbjerg split the Terriers defence with one pass, Terence Kongolo got his legs in a twist and Redmond ran through before smashing in his first goal of the season.
Redmond was having a fine game and he seized on more hesitant Huddersfield play to get in another shot, this time over the bar, before the visitors doubled their lead.
Mathias Jorgensen stuck out a leg just inside the box and Ings went over it before coolly rolling his penalty inside the post.
Huddersfield at last forced Alex McCarthy into action in the 55th minute and the Saints keeper responded with a terrific save, sticking out a hand to keep out Jorgensen's close-range header.
Three minutes later the hosts found their breakthrough. Billing was a long way out when he let fly but McCarthy, whose line of sight may have been blocked by Jan Bednarek, took a step the wrong way and Billing's shot flew past him and into the middle of the goal.
Huddersfield almost had a second immediately but this time McCarthy got behind Isaac Mbenza's fierce shot and pushed it out for a corner.
The buoyant mood around the stadium was punctured again in the 71st minute, though, when Saints scored their third goal.
Obafemi had only been on the pitch for seven minutes after replacing Ings and had already pulled a shot wide of Lossl's goal.
While this was a special moment for the teenager, it was a horrible one for Terriers captain Christopher Schindler, who tried to turn out of trouble in his own area but was robbed by Redmond and the wideman set up Obafemi to slide the ball past Lossl.
Obafemi was denied a second by Lossl but that would merely have added gloss and the afternoon ended with the Saints fans waving their Santa hats in the air in triumph.