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.
Ward, signed a couple of days ago from Wolves on a season's loan, was involved in setting up several promising attacks which put Birmingham's reconstructed defence under pressure.
That was demonstrated in the 16th minute when Will Buckley's left-wing cross was headed by Leonardo Ulloa towards the far corner of the net only for Darren Randolph to push the effort wide of the post.
Ulloa, however, made a mess of a golden opportunity after 20 minutes. Sent clear by David Lopez he stumbled and sent his bobbling shot wide of the post in what was a massive let off for Birmingham.
At the other end the home side's attack struggled to cause many problems in the first half for a Brighton defence including former Blues stalwart Matthew Upson.
It was not until the opening five minutes of the second period that Birmingham finally found their shooting boots, only to see two efforts hit the frame of the goal.
Andy Shinnie latched onto a Scott Allan pass in the 49th minute before crashing a shot against the top of the bar - a fate which also befell Lee Novak a minute later.
On both occasions Brighton's defence was caught stranded in midfield but they rode their luck to stay in the game.
They quickly regrouped as the game became more open with both teams desperate to score the opening goal.
On the hour it required a superb save by Randolph to batter down a shot on the run from Kemy Agustien.
But Agustien was the player who created the breakthrough in the 73rd minute. He put a pass into the path of Crofts who scored with a low measured cross shot to the right of Randolph.