Cardiff started with Jay Bothroyd as skipper and Michael Chopra on the bench.
A fairly even first half saw Cardiff have more direct efforts on goal but the game remained in the balance.
The second half became stretched and Cardiff were quick to exploit the spaces appearing the in the Bristol defence with Chopra and McCormack creating several decent chances. The goal aside McCormack hit the bar, Chopra missed a point blank volley, failed to twice beat the keeper when closing in on goal and a Bothroyd header was just over.
Bristol City got the ball forward but were seriously lacking in front of goal and never forced Marshall into any heroics.
The goal when it came was created by Michael Chopra, he broke into the right hand side of the box, shot across the keeper only to see the ball hit the post. Fortunately for City the visiting defender Bradley Orr was unable to do anything other than knock the ball into the empty net.
Four mins of added time edged towards 5 but City didn't let it slip this time. The counter attacking by the Bluebirds was great to watch and with the two sets of fans goading each other after Cardiff's goal the atmoshpere became pretty good for a 1/4 full stadium.
So now Cardiff have another game this Saturday with Leicester City the visitors in the 4th round. The next Leage action is on Tuesday when we are back at Ashton Gate for the third game against Bristol City in 15 days.
Tickets for the Leicester game are available now online and from the ticket office from Wednesday.