It was often a frustrating game and Coventry paid a heavy price for a lapse of concentration which allowed Fahey to score the winner.
Birmingham manager Chris Hughton, was delighted with the first league win achieved since his appointment.
He said: "It was very nice to collect the three points but importantly we have two tough away and that is why we had to beat Coventry.
"Over the 90 minutes I thought we deserved the win and sending on Adam Rooney was a game-changing move.
"I thought he came on and displayed a lot of energy and certainly changed the game for us.
He did well in the lead-up to the goal scored by Fahey and Hughton added: "Rooney is a lad who scored a lot of goals in Scotland but with our three strikers out of action he has had a lot of responsibility from day one in pre-season."
Surprisingly Birmingham again had Scott Dann, who has been attracting the attention of Arsenal this summer, on the bench when they could have used his defensive skill.
Coventry, following a dismal start to the season when they lost their two opening games, gained in confidence in the closing stages of the goalless first half as Birmingham ran out of ideas.
On two occasions the home side were indebted to goalkeeper Boaz Myhill, who had to dive to his right to keep out a stinging Sammy Clingan free-kick.
On-loan Myhill then had to move smartly to save a 30 yard blockbuster from former Birmingham winger
Birmingham, operating a defensive 4-5-1 formation, often frustrated their fans with some negative play as they struggled to impose themselves against a struggling Coventry outfit.
With Fahey having an off-day before his goal Birmingham posed few problems and it not until the 50th minute that they had their first real chance to go ahead when teenager Chris Wood forced Jean Beausejour's left-wing cross over the bar from close range.
Birmingham's first effort on target did not arrive until the 62nd minute when Morgaro Gomis fired in a long-range effort which Joe Murphy dived to turn around the post.
A casual Myhill very nearly carried a Chris Hussey cross over the line as Coventry produced several counter-attacks in an attempt to break the stalemate.
It was a tactical switch which enabled Birmingham to steam into a 72nd minute lead.
Rooney took over from Wood and quickly produced a header from Liam Ridgewell's cross which hit the post - and from the rebound the onrushing Fahey blasted home his first goal of the season.
Coventry manager Andy Thorn was not downhearted with the result.
He said: "Everything is stacked against us at the present time but I have good bunch of lads and if continue to apply ourselves we will start picking up the points.
"We controlled our own performance and frustrated Birmingham. We just switched off for a couple of seconds and the ball finished in the back of the net.
"I thought Sammy Clingan ran the game and apart of the result I cannot fault the players."