Shane Long came close for Southampton and Aaron Mooy forced a good save from Angus Gunn at the other end before Redmond fired the home side into a 40th-minute lead with a goal of the highest quality.
The forward cut inside before he fired the ball into the top corner past visiting keeper Joel Coleman, who kept out an almost identical effort by James Ward-Prowse shortly after the break.
Huddersfield took advantage and equalised in the 55th minute after a howler by Gunn.
He was slow to react to a simple back pass by Ryan Bertrand and Pritchard capitalised as he got to the ball first and rolled it into an empty net after rounding the keeper.
Striker Charlie Austin missed Southampton's final chance to snatch a late winner, bending his shot wide in stoppage time.
(Writing by Zoran Milosavljevic; Editing by Ian Chadband)
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