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.
More top news
Staff and patients at Southampton General Hospital are being urged to be vigilant after a woman was attacked in broad daylight
On your marks- runners get set for 10 mile challenge
The locker key was found on the body of Southampton man who died when the Titanic went down