The pre-season arrival from Deportivo La Coruna produced a fine diving header to complete the turnaround after Mathias Jorgensen's opener, the fastest Premier League goal this season, was cancelled out by Shane Duffy.
Jorgensen struck after just 55 seconds but David Wagner's side conceded on the brink of half-time following Steve Mounie's red card for a foul on Yves Bissouma.
And Andone came up with the winner on his first start as the visitors' numerical advantage told, bringing a halt to the Terriers' recent revival and giving Chris Hughton's men their first win since October.
The deadlock was broken inside the opening minute as Bruno attempted to clear but succeeded only in sending the ball into the heart of his own penalty area, where Jorgensen leapt above Mat Ryan to head home.
A fine save from Jonas Lossl and follow-up block by Jonathan Hogg denied Duffy and Andone in quick succession as the hosts somehow held firm.
Mounie's dismissal tested their resolve further still, the Benin international given his marching orders after his tentative challenge resulted in his foot making contact with Bissouma's shin.
The 10 men went close to doubling their lead just before the break, but Aaron Mooy's free-kick was tipped to safety by Ryan.
That proved a telling save as Brighton levelled it up in first-half-stoppage time courtesy of Duffy's bullet header from Solly March's cross, which came after Bruno had won and taken a quick corner.
Lossl came to Huddersfield's rescue early in the second half to repel Bissouma's volley but was helpless to keep out Andone's header from March's pinpoint delivery.
What does it mean? Terriers tamed, Seagulls soar
Huddersfield had taken seven points from their last three outings, lifting them out of the relegation zone, but this was a reality-check for the Yorkshire club. It was a timely victory for Brighton, too, as they would have been only two points ahead of their hosts had they lost.
March to victory
Both of Huddersfield's goals owed much to the quality of the deliveries from March, whose accuracy at picking out his team-mates in a crowded penalty area made all the difference in a game of fine margins.
Bruno's mishit clearance created danger where there was none and put his side on the back foot almost straight away. It left Brighton with an uphill struggle, although he did to his credit play a role in their equaliser.
Key Opta Facts
- Huddersfield have won just one of their last 10 Premier League home games, drawing two and losing seven.
- Brighton have scored in seven consecutive league games for the first time since February 2017, when they put together a run of nine.
- March has registered four assists in his last four league appearances, two more than he managed in his previous 46 top-flight games (2).
- Andone is the first Romanian to score in the Premier League since Vlad Chiriches netted for Tottenham against Fulham in December 2013.
Huddersfield head to Bournemouth on Tuesday while Brighton host fierce rivals Crystal Palace with the Premier League's top half in their sights.