Southampton, who ended Arsenal's 22-game unbeaten run last time out, secured consecutive league wins for the first time in 20 months and they achieved it with a dominant performance at the John Smith's Stadium.
Southampton went ahead against the run of play in the first half, as the lively Redmond ran on to fellow midfielder Pierre-Emile Hojbjerg's through pass and finished emphatically past goalkeeper Jonas Lossl in the 15th minute.
They doubled their lead three minutes from the break as Ings slotted home from the penalty spot for his seventh league goal of the season, after being brought down by Huddersfield defender Mathias Jorgensen's clumsy challenge.
Huddersfield reduced the deficit to 2-1 after the restart as midfielder Philip Billing's swerving effort from distance flew past Southampton goalkeeper McCarthy, who appeared to be unsighted by a team mate.
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Southampton then failed to deal with a long throw and nearly paid the price as Jorgensen's header from point blank range was swatted away by McCarthy.
The hosts grew in confidence as they pushed for an equaliser but it was Southampton who restored their two-goal advantage in the 71st minute, as substitute Michael Obafemi calmly finished from close range after good work from Redmond inside the box.
Ireland international Obafemi, who became Southampton's youngest Premier League goalscorer at 18 years and 169 days, could have doubled his tally in the 86th minute after being played through but he could not find a way past Lossl.
Victory lifted Southampton to 16th in the table with 15 points from 18 matches.
"It was a deserved win for us. We played a fantastic first half with fantastic goals... the guys worked very hard today," Hasenhuettl said.
"We have very good options (in attack) when we win back the ball. The passion, character and mentality of our defence was good too... it was an aggressive atmosphere and we knew we had to do our best.
"It's a very important step for us and I hope it will go on like this."
Huddersfield have now lost each of their last five league matches to sit second from bottom with 10 points.
"We have to criticise ourselves today... this is a tough time at the moment," Huddersfield manager David Wagner said.
"We've to make ourselves independent from the circumstances and perform again. We have to show we have learned from this lesson today... we were not brave enough."
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond and Martyn Herman)
