Cardiff boss Malky Mackay was determined not to make too much of the fact his team now lead the way in the table.
"I was delighted tonight. I always knew it was always going to be a tough game for us," he said.
"It's nice to be up there but it's about being consistent. There's a long way to go so nobody's getting carried away about being top of the table."
He felt his side could have taken tension out of the closing stages by putting away earlier chances.
"We should have been out of sight, we shouldn't have had to defend in the last five minutes," he said.
"There were four or five chances that flashed across their box that we should have dispatched, but overall I'm very happy."
Thrilled for Hudson, Mackay said: "He's someone that is always a threat when he goes up for set-pieces."
Mackay also enthused over the performance of veteran Bellamy, the 33-year-old former Liverpool and Newcastle forward proving instrumental in the victory.
The Bluebirds boss said: "I thought he was like a 20-year-old tonight at times. His closing down is exceptional.
"Everything starts with hard work. If you look at things slightly differently sometimes you see other traits in players other than to just say he is a good player."
Birmingham City manager Lee Clark
"The performance was there again today. The last two games I've seen bright signs - our performances have been good.
"We've come to two very tough places and been more in the game. We've handled the opposition very well and I certainly feel we should have got something from this game, which would have been two positive results.
"I think we deserved something from the game. I thought we played well and we just got a bit unlucky. The goals are disappointing from our point of view but I feel we deserved at least a point."
Clark said, according to www.bcfc.com: "When you get back in the game and five minutes afterwards you go 2-1 down - it's tough. We should have dealt with the corner better."