Following the result, the Seagulls have moved into the playoff places, one point ahead of Reading, who have dropped out of the top six due to a defeat to Wigan Athletic.
Huddersfield took the lead in the sixth minute of the clash when Oliver Norwood found the back of the net from a 25-yard free kick.
Brighton ended the first half on the front foot, but they failed to find the breakthrough before the break, which caused their momentum to disappear.
After the half-time interval, Huddersfield were comfortable in possession, while Brighton struggled to make an impact in the final third.
The home side were close to doubling their lead when Norwood lined up a free kick in a dangerous area, but his whipping effort produced a fine save from Tomasz Kuszczak.
As the game reached the closing stages, Bruno Saltor was able to clinch a goal for Brighton and push them clear into the top six, while Huddersfield have now stretched their gap from the relegation zone to nine points.