Defender Burn scrambled home the only goal of the game, via a Danny Seaborne deflection, against the club he steered into the Sky Bet Championship with his Wembley header against Brentford in May.
The Glovers made no bones about their desire for Burn to return to Huish Park but the Fulham prospect instead chose to head to St Andrews on loan, much to Clark's delight.
He said: "He has been absolutely magnificent for us in our three competitive games, I thought he looked very, very mature for his age and he handled everything they threw at him, whether it was the small tricky players or the big lad they put on.
"He has certainly improved, I think he's just getting better and better and I hope he has a similar season for Birmingham as he did for Yeovil last year.
"Then he will go back to Fulham and push for the Premier League squad so at the minute it is benefiting everybody. But I thought all the defence were great today and when they did break through, our keeper was there.
"We are up and running and we were resolute. We are happy to win the game we didn't deserve to lose last week and I was a little bit unhappy and, however we win it we have got to win it - we need to keep working hard."
The Glovers were entertaining a near-full house for their first home game in the Championship and it was Gary Johnson's men who enjoyed the better of the first half.
However, they were dealt a blow on just six minutes when keeper Marek Stech had to be replaced by goalkeeping coach Gareth Stewart due to a broken hand which will keep him out of action for three months.
Yeovil boss Johnson felt that his side more than matched their former Premier League opponents on the club's first ever home game in the second tier, and he labelled the defeat as three points lost.
He said: "We looked competitive which is what we needed to do but we looked like, for me, as if we could win that game.
"We could have won that game looking at the two teams: our tactics, their tactics, and it was three points lost for us.
"That's not me making it up that's my honest belief.
"We didn't really look potent enough for the whole game. I would have liked to get past people more and when we did get through we didn't create chances.
"We did compete and it was fantastic to see the atmosphere, hopefully they will keep with us because we more than matched a Birmingham side, but to be better than them we needed to be more competitive."