A goal in either half from Nikola Zigic and Chris Burke earned the points and left Clark purring.
Birmingham boss Lee Clark said: "You have to be delighted to win 2-0 on the road and that's certainly how I feel right now.
"A second successive clean sheet was particularly pleasing as solid defending is always the basis for success in football.
"We came here with a game plan and executed it very well. We had some outstanding performers, not least Chris Burke who has been back to his fine form of last season in recent games.
"We've only lost once in eight games but we won't get ahead of ourselves. It's been an up and down season and we can only focus on the next game against Hull.
"It was a big boost to hear that George Boyd had left Peterborough during the week. He is a terrific player who I've had my eye on for years but never had the opportunity to sign.
"But we'll still have to face him next Saturday now he is at Hull and that will be a really tough game after their result."