Hughton, making his competitive bow at St Andrew's on Saturday, can be credited with the inspired introduction of substitute Adam Rooney which led to the vital breakthrough in an evenly-fought Championship clash.
The summer signing stepped off the bench in the 68th minute and wasted little time making a difference, heading against a post before reacting quickest to tee up the rebound for Fahey to smash home from 10 yards.
The winner came after both sides had wasted a golden opportunity apiece to seize the initiative, Lukas Jutkiewicz and Chris Wood firing off-target when they really should have done better.
Victory gets Birmingham off the mark in what will be a tough quest for an immediate return to the Premier League, although concern will be growing just 22 miles down the road for a Coventry side who were more than a match for their local rivals but have now lost their opening three matches of the season in all competitions.
Rooney's relegation to the bench in favour of on-loan West Brom striker Wood was Blues' only switch from last weekend's 2-1 defeat at Derby, while skipper Sammy Clingan's return from international duty was Coventry's only change to the side who lost 3-1 at Bury in the Carling Cup in midweek.
Striker Marlon King, who angered Sky Blues fans by controversially switching to Birmingham over the summer, missed out with his troublesome knee problems, while Birmingham's prized centre-back Scott Dann found himself on the bench against his former employers for a second successive weekend.
However, there was a start in Coventry's XI for former Blues winger Gary McSheffrey.
Visiting striker Jutkiewicz should have broken the deadlock in the 17th minute, firing the best chance of the first half wide from 10 yards with his favoured left foot.
At the other end, Wood rose to direct a free header straight at goalkeeper Joe Murphy.
But it was Coventry who probably shaded a finely-balanced opening 45 minutes, McSheffrey's long-range effort forcing a fine parried save from Boaz Myhill.
Blues failed to really get any kind of momentum going in the first half but they certainly livened up after the restart and Wood wasted the clearest of openings in the 51st minute.
Jean Beausejour sent a ball in from the left and the New Zealand international somehow blazed the ball over the crossbar from a great position.
Morgaro Gomis saw his effort tipped around a post by Murphy while Coventry's rearguard produced more than one timely block, with McSheffrey firing wide for the visitors.
Hughton brought on Rooney and the former Inverness man was instrumental in what proved to be the winner for Fahey.
Blues slowed the game down over the remaining 15 minutes and, with Jutkiewicz heading a late Clingan corner over the crossbar, duly walked away with all three points.