Beram Kayal fired Albion into the lead after just 18 seconds and he again went close on 11 minutes when his shot was deflected just wide.
Sam Baldock was then twice denied by Huddersfield keeper Joe Murphy, before the hosts’ Jacob Butterfield curled a free kick just wide.
Butterfield levelled on 54 minutes with a shot from a tight angle and Albion keeper David Stockdale then made a decent save to deny Nahki Wells.
Albion pressed for a late winner and Chris O’Grady flicked a header just over, before Murphy collected Kazenga LuaLua’s injury-time effort.
Brighton boss Chris Hughton said: “At the start of the season, if you had said we would have seven points from nine and we’d be second at this point before the season started, especially with two of the games being away from home, then I would have been delighted. We have to remember we have only had one home game so far.”
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