Pep Clotet praised his Birmingham players for sticking to their game plan after a shock start as they came back to win 3-1 at Ashton Gate.
Bristol were in front inside a minute, Jamie Paterson racing onto a poor back-pass from Marc Roberts to round goalkeeper Lee Camp and shoot into an empty net.
But after 23 minutes Dan Bentley could only parry a left-footed drive from Jeremie Bela and Scott Hogan was on hand to equalise.
Birmingham took the lead on the half hour as Andreas Weimann got his head to a Jude Bellingham cross from the right and only succeeded in glancing the ball into his own net.
And in stoppage time Lukas Jutkiewicz turned Filip Benkovic on the edge of the box before neatly beating Bentley from close range.
Clotet said: “I have the honour to be coaching a group of players who don’t let mistakes like the one we made at the start affect them.
“They are so resilient and it showed in overcoming the unfortunate incident that led to the first goal. If it hadn’t been for that moment, we would have had a deserved clean sheet.
“What pleased was that we didn’t let the first goal affect the way we wanted to play the game. The players stuck to our plan and put it into effect really well.
“Bristol are a very good side and played well, but we had a bit of luck with the own goal and defended really strongly when we needed to.
“We knew they would go to three at the back and throw everything at us in the second half so we were well prepared for that.
“We are not at Bristol’s level yet, but we worked on areas where we might tactically be better and that helped get us the result.
“They are one of the most difficult sides to play against in the Championship, so to come here and get such a good result is very pleasing.”
Bristol head coach Lee Johnson introduced two of his January signings, Nahki Wells and Benkovic after 58 minutes, but neither impressed.
Johnson said: “We made some poor decisions after taking the lead and didn’t defend well.
“One or two individuals were off their game tonight and I didn’t like their performance or their attitude.
“So we found ourselves behind at the break and, although we had a great chance to equalise through Famara Diedhiou, our delivery into the box wasn’t good enough.
“You have to give Birmingham credit. They are a strong side and they played well. But there is no hiding the fact that I am disappointed.
“We were poor in the first half and I had to throw caution to the wind with the substitutions earlier than I would have liked.
“They worked to an extent, but we ended up chasing the game and were caught out when we poured forward at the end.
“I am not going to throw the baby out with the bathwater because we have been on a good run.
“It’s a punch on the nose that we need to recover from quickly and go again against Derby next Wednesday.
Bristol’s best chance to equalise came after 81 minutes when Diedhiou chested down an Ashley Williams chip only to volley over from 10 yards.
“That was the key moment,” said Johnson.