Doyle scored his first goal for the club just after half-time before winning a penalty that Peter Whittingham converted with 15 minutes to go to put the game beyond the reach of the Blues.
It ended a run, stretching back to January 10, of seven home games without a win for the Bluebirds in all competitions.
Bluebirds assistant boss Young said: "Since the New Year we've been in good positions in a few home games but not quite got over the line so it's very pleasing to get the win.
"I thought Eoin and Matthew Kennedy changed the game for us when they came on.
"Eoin has been very unlucky not to get on the scoresheet since coming to the club in January but we have always known he has plenty of quality.
"He made a real impact and it's nice to see him get the goal his performance deserved.
"As a side we are showing a lot more resilience and to get another clean sheet is very good.
"The whole team is working hard and we want to finish as high up the league as possible."
Birmingham manager Gary Rowett refused to do the post-match press conference after being sent to the stands for arguing with the referee in the second half but assistant manager Kevin Summerfield was scathing about his side's display.
Summerfield said: "This will be a kick up the backside for us, the players will really have to roll their sleeves up now for the rest of the season because it will have a big impact on what happens next year.
"That performance was not up to the standards that we have set ourselves this season.
"Our passing and general play was not right, we tried to change the system a little bit and maybe that had a big effect on the players.
"But the players have to take some responsibility, they should be frustrated with that performance and we have made sure they are aware of that.
"Gary was obviously very frustrated, there was a throw-in that had gone out of play next to us which we felt was clearly our ball but the assistant referee gave it the other way.
"He (Gary) did not swear but he made the point to the referee that the assistant referee and linesman were far away but he threw the ball down and that was enough to see him get sent to the stands.
"We are not going to blame the referee for the defeat, they have only got a few seconds to make a decision but we didn't think it was a penalty and that killed the game off."