However, a straight red card for Steve Mounie for a careless high challenge on Yves Bissouma turned the tide in favour of the visitors.
Duffy put Brighton level deep into first-half stoppage time, heading home Solly March's cross after Bruno cleverly won a corner and took it quickly to create the chance.
March was again the provider in the second half, whipping in another cross for Romanian striker Andone to stoop and head home the winner, and his first goal for the club, in the 69th minute.
"When I signed for the club, I waited a long time for my opportunity and now I am very happy. It is perfect. I have my first goal," the 25-year-old striker said.
Huddersfield manager David Wagner fumed about the performance of referee Michael Oliver.
"All the big ones against us, he got wrong. This is why at the moment football is no fun; absolutely no fun," he said.
"The referee has a big part to play and I don't think he did his best, even if he didn't mean to."
The win lifts Chris Hughton's side to 11th place in the table on 18, while Wagner's Huddersfield are once again hovering above the drop zone in 17th place on 10 points.
(Reporting by Philip O'Connor; editing by Clare Fallon)
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