Birmingham, who also lost their opening home match 1-0 to Watford, could count themselves unlucky as they twice hit the woodwork in the second half but it was Crofts' clinical 73rd-minute strike which proved the difference as new Brighton coach Oscar Garcia celebrated his maiden win in the hotseat.
Brighton, a side loaded with experience, included the two Irish internationals, Stephen Ward and Keith Andrews, for their first full appearances and it paid off handsomely with three points.
Both were prominent in the early stages when the Seagulls' smart play indicated a hard afternoon for the home club.
Defeat in head coach's Oscar Garcia's first league game in charge at the Amex Stadium 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.
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.
Derby responded positively to going behind, however, and their adventurous style of play saw them pull level nine minutes later.
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.
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.
The midfielder's decisive strike earned a 2-1 win over last season's beaten play-off semi-finalists, sending the majority of a sold-out Elland Road into delirium on a day which had been heralded as the first of a new era at the club.
Leeds had not appeared so sure-footed early on, however, and it was Brighton who made the first impression as Andrea Orlandi forced Kenny into action from 25 yards.
The early stages certainly gave a nod to Garcia's philosophy - Brighton were happy to roll the ball around - and with 13 minutes gone it bore fruit as Ulloa haunted Leeds again.
Brighton had been largely contained since their goal at that point, but suddenly reintroduced themselves to the game at the three-quarter mark with only Kenny stopping them from regaining the lead.
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Their dreams of promotion may be over, but Sussex Police are thanking Brighton and Hove Albion fans for staying out of trouble. Officers made a total of six arrests at the game at the Amex last night.
Chief Inspector Paul Betts, said: "There were a few sporadic incidents following the match, but these appear to have mostly been amongst groups of disappointed fans and not from clashes between the groups. We also dealt with a number of incidents on board trains leaving Falmer in both directions."
Sussex Police were joined by colleagues from five neighbouring forces, including mounted officers from Thames Valley. Six arrests were made, five at the Amex Stadium and one in Surrey Street, Brighton.