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.
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Thursday afternoon's weather for the west of the region
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Mark Love has been found guilty of the horrific attack and murder of Roy Blackman, an elderly businessman, at his home in Biddenden in Kent