Defeat in head coach's Oscar Garcia's first league game in charge at the Amex means Brighton have lost all three of their opening Championship and cup games.
Derby, who drew their opening game at home to Blackburn, settled quickly but failed to make the most of a surging run and cross from former Watford defender Craig Forsyth in the second minute.
Brighton's Spanish playmaker David Lopez, back in the midfield with Latvian Vitalijs Maksimenko, had a shot from the edge of the area blocked before Derby's new Scottish striker Johnny Russell - a £700,000 buy from Dundee United - flashed a left-footed shot wide.
Derby midfielder Paul Coutts saw a 25-yard shot deflected over the bar but the Rams were shaken when Argentinian striker Leonardo Ulloa broke the deadlock in the 18th minute.
Ulloa, who spearheaded the Seagulls promotion challenge last season with 11 goals in 21 games, gave goalkeeper Lee Grant no chance with a stooping header following a pinpoint cross by Spanish defender Inigo Calderon.
Ulloa skilfully got a yard of space from his marker before finding the back of the net for his second goal of the season.
Derby responded positively to going behind, however, and their adventurous style of play saw them pull level nine minutes later.
Good work down the left wing by Forsyth set up Martin at the near post and, after his initial shot was blocked, the former Norwich striker coolly fired home into the bottom of the net from close range with the outside of his right boot.
Brighton were awarded a free-kick on the edge of the area shortly before the break when Derby skipper Richard Keogh was harshly penalized for a challenge on Ulloa, but Lopez's goalbound effort was blocked.
Derby had given as good as they got in an evenly contested first half and Scottish midfielder Craig Bryson fired over after Coutts and Martin had linked up intelligently.
The Rams would take the lead with a superbly worked goal only two minutes after the break.
A storming run by Kieron Freeman down the right wing led to his excellent cross being sidefooted home by Martin at the far post.
Brighton, giving the ball way too cheaply, struggled to impose themselves and a free-kick from Lopez was scrambled clear before winger Will Buckley's angled shot was parried by keeper Grant.
Keogh put a header over for Derby following a free-kick from Coutts before Ulloa almost pulled Brighton level when his powerful header from 12 yards cannoned back off the post.
Brighton's former Swansea midfielder Kemy Agustien had a fierce drive tipped over by Grant and Calderon's deflected effort flew over as the Seagulls began to raise their game.
Substitute Jamie Ward threatened to add a third Derby goal late on but desperate defending at the far post robbed him following a cross by Coutts.