Marc Nygaard?s goal just after half-time gave Rangers only their second win in 10 matches.
Nygaard headed home Lee Cook?s cross after returning to the starting line-up along with Marc Bircham and Matthew Rose.
Cardiff went close when Jason Koumas fired a 30-yard free-kick just wide and Rangers keeper Simon Royce produced saves to deny Koumas and Cameron Jerome.
Rangers had chances to score a second goal. Neil Alexander saved from substitute Shabazz Baidoo and Martin Rowlands blasted over from 10 yards.
‘It was nice to get what we deserved because in the last few weeks that hasn’t happened,? Ian Holloway said.
‘I couldn’t be more chuffed if I were a badger at the start of the mating season.
‘It was great to get some of my boys back. I made some changes and they showed me some character.?
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