A single goal by Â£1.7million striker Peter Thorne settled this first leg play-off tie as Cardiff City go to Ashton Gate for the return on Tuesday with a slender advantage.
Thorne rose to thump a Willie Boland cross high into the net in the 78th minute to seal a vital victory for the Bluebirds. In fact it was the first time Cardiff had beaten Bristol City since April 1971, 22 games ago.
"I would have settled for a 1-0 victory before the game and the scoreline was an accurate reflection of the play," said Cardiff boss Lennie Lawrence.
"Bristol City weren't as dangerous as they have been in the past, but we also worked hard to keep that clean sheet.
"Peter Thorne is a class act and he now has 16 goals for the season to add to all the hard work he does around the field.
"2-0 would have been an injustice to Bristol City but we will try to win the tie on Tuesday.
"I am very pleased that we played the first game at home and the fans were excellent and got right behind the team.
"We have a lot of experience at the club and we all know there is a long, long way to go. I brought two subs on, just to provide fresh legs.
"There are no injury worries and I am very happy that everything went right today including team selection and tactics.
"I am no more or less confident than I was before today but I am so happy that we won. We came into the play-offs on the back of some indifferent form but it is what you do on the day that is important." Cardiff's man of the match was centre-back Spencer Prior who has fought back from a period of poor form to become once again one of the crowd's favourites.
"We are very committed as a team, but know we are only halfway there and need to carry it on in the next match," said Prior.
"Bristol City have been our bogey side but we deserved to win today. The goal we have scored today does not change the way we have to approach the second leg, but as long as we are disciplined we have a good chance of getting through to the final." Bristol City manager Danny Wilson was in positive mood, despite his side returning home with a one-goal deficit.
"It was a very close game and tight in most areas with very few clear-cut chances," he said.
"We are unfortunate not to come away with a 0-0 draw, but it was an exciting match fully committed and played in a very fair manner.
"There were two good sides out there today and the second leg will be just the same, but at least we now know what we have to do.
"1-0 will give Tuesday's match an edge but at home I am sure we will be able to create chances.
"I am a bit disappointed that it was a mistake that led to the goal, but the tremendous atmosphere inside the ground didn't phase us and we coped with the pressure very well.
"There is a long way to go before the tie is over and we don't need to chase the game in Bristol."