In a game of few real opportunities West Ham sealed the three points with a controversial 69th minute penalty from Mark Noble.
It was something of a disputed penalty as the luckless Birmingham goalkeeper, Colin Doyle, cut across Craig Bellamy as the ball was going out of play.
Newly-promoted Birmingham are now without a win from their first three games which is something of a repeat of their form when they were relegated two seasons ago.
Curbishley himself cut a lonely figure sitting alone in the stand, watching a desperate first half that struggled to come to life in the heavy rain, but his second-half appearance on the West Ham bench appeared to have the desired effect.
One bright spot for Curbishley was the form of his skipper, Matthew Upson, who was a given a rough ride by the Birmingham fans on his return to St Andrew's.
It was the sterling work of Upson which kept West Ham in the game, while the industrious Noble deservedly emerged as the Hammers matchwinner.
The expensively assembled West Ham side included their latest signing, Kieron Dyer, but he had a quiet debut against the mobile Birmingham defence.
Noble was the one player to pose any real threat to Birmingham, while Bobby Zamora carelessly wasted a couple of good goal chances in the second period.
Birmingham battled hard but their attack lacked a cutting edge and West Ham's goalkeeper, Robert Green, only had one save to make in the match when he went down low to keep out a free-kick from substitute Gary McSheffrey.
The Midlands club struggled to make an impact particularly in midfield where French international, Olivier Kapo, drifted in an out of the game. As a result, there was a serious lack of service to their strikers and his performance must be the cause of some concern.
Scottish international Garry O'Connor made his first start but the former Lokomotiv Moscow striker failed to get in a single goal attempt.
With the game drifting to a goalless draw the match was turned on its head when Doyle, who was at fault with two goals in the opening game at Chelsea, cut across Bellamy.
Referee Mark Halsey delayed his decision until the linesman indicated a penalty. Noble grabbed the ball and powered a low shot to the left of Doyle who went the wrong way.
Birmingham themselves claimed a penalty when O'Connor was pushed in the back by Zamora but on this occasion Halsey declined to consult his linesman and a frustrated Blues must have realised that it was not their day.
Doyle later atoned for his earlier mistake with two last-minute saves from Zamora and Bellamy.