Graham Kavanagh netted the only goal of the game from the penalty spot two minutes before the break.
The win lifts The Bluebirds up to seventh spot in the table and back in the play-off race.
Wycombe's play-off hopes suffered a major blow when they were thumped 4-1 by Blackpool at Adams Park.
Scott Taylor gave the Seasiders the lead after 20 minutes and a brace from striker Richard Walker (23, 48) put the visitors in firm control.
Jermaine McSporran pulled one back for the home side eight minutes from time, but John Murphy restored Blackpool's three-goal lead with the fourth five minutes later to give Steve McMahon's side all three points.
Northampton boosted their survival hopes as they climbed out of the bottom three with a hard-fought 2-1 win over Peterborough.
Jimmy Bullard had given the visitors a dream start with the opening goal after just two minutes, but Sam Parkin drew the sides level in the 17th minute.
Jamie Forrester hit the winner for Northampton after 38 minutes to help them climb above Wrexham to fourth from bottom.
Oldham missed the chance to move into the top six when they were held to a 1-1 draw by Tranmere at Boundary Park.
Veteran striker Paul Rideout gave Rovers the lead after 12 minutes, but Argentine loan signing Cristian Colusso grabbed an equaliser for the home side with his first goal for the club on the hour mark.
Notts County remain second from bottom after falling to a 3-1 defeat to Wigan at Meadow Lane.
Lee McCulloch fired the visitors in front after 15 minutes and the home side's hopes of getting anything from the game suffered a blow when Ian Baraclough was sent-off four minutes into the second half.
County made light of their numerical disadvantage to draw level through Ian Richardson in the 63rd minute.
Gary Teale restored The Latics' lead nine minutes from time and Paul Daglish made sure of victory with the third in the dying moments to keep alive Wigan's hopes of making a late push for a place in the play-offs.
Click on fixture for full match summary
Cardiff 1-0 Bury
Northampton 2-1Peterborough
Notts County 1-3 Wigan
Oldham 1-1 Tranmere
Wycombe 1-4 Blackpool
Click here for updated league table
