Andone rose to meet Anthony Knockaert's chip to power home from near the penalty spot just when it looked like Brighton's familiar failings in front of goal might again deny them.
Before the game, locally-born world boxing champion Chris Eubank Jr was introduced to the crowd in the hope that he would inspire a fighting performance from a side who had secured just two points since the start of the year.
But Brighton again struggled for a knock-out blow in a lucklustre first half with Iranian Alireza Jahanbakhsh providing the only excitement when his 41st-minute shot fizzed against the bar.
Huddersfield, who beat Wolverhampton Wanderers in midweek, were forced into a change with Aaron Mooy replacing the injured skipper Jonathan Hogg.
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The Australian had little chance to shine as Brighton cranked up the pressure after the break with Andone having one effort well saved by Jonas Lossl before he finally beat the keeper for the win that moves Brighton five points clear of the drop zone.
Huddersfield remain adrift at the bottom, 13 points behind 17th-placed Southampton.
(Reporting by Neil Robinson; Editing by Ian Chadband)
