The hosts climbed out of the relegation zone and up to 19th with only their third win of the season as debutant Sol Bamba proved to be the match-winner.
Cardiff's new era was reflected in Warnock's maiden team selection, with new signings Bamba and Junior Hoilett being thrown straight into the starting lineup and Joe Bennett also being handed a full debut for the Bluebirds.
However, clear chances were few and far between for both sides in the first half, with Bristol City seeing more of the ball and Cardiff offering the slightly greater threat in the final third.
Warnock has not lost his first game in charge of a club since February 1997, and he moved a step closer to extending that record when the hosts took the lead after 25 minutes when Peter Whittingham calmly rolled a penalty into the bottom corner.
Craig Noone had won the spot kick for his side when he was tripped after slipping the ball through the defender's legs, and Whittingham made no mistake from 12 yards, sending the keeper the wrong way.
The long-serving midfielder was only the fourth separate player to score for Cardiff this season, and the first to do so at home after their only previous goals in South Wales had been own goals from Shane Duffy.
The Bluebirds threatened a second goal shortly after the half-hour mark when Sean Morrison's header from a Whittingham corner landed on the roof of the net, while Joe Ralls also came close on the stroke of half time with a curling effort into the arms of Frank Fielding.
Bristol City have rescued a league-high 11 points from losing positions so far this season, but they failed to have a single shot on target in the first half and showed few signs of improving that statistic after the interval either.
Noone curled one effort wide early in the half, but once again there was a relative lack of goalmouth action at either end until Cardiff doubled their advantage.
It was Bamba who marked his debut with a goal, reacting quickest after Lambert's effort had been tipped onto the crossbar to flick the ball home from close range.
Lee Johnson's side should have rescued a point late on too when Joe Bryan burst down the left flank before sending a low cross into the middle, but Bobby Reid somehow put his close-range effort over the crossbar in the final minute of normal time with the goal gaping.
Seven minutes of added time gave Bristol City another glimmer of hope, but they were unable to find an equaliser as their four-match winning streak came to an end at the hands of their Severnside rivals.