Campbell, 25, for whom Cardiff recently paid an undisclosed fee to Sunderland, capitalised on a defensive mix-up to convert from six yards just two minutes after replacing Bo-Kyung Kim in the second half.
Malky Mackay's side have now dropped only two points in their last seven matches, but by no means had it all their own way at Elland Road and needed a fine late save from goalkeeper David Marshall from Tom Lees' header as they extended their unbeaten league run to seven matches.
Marshall also pulled off a superb save to deny Leeds midfielder Ross Barkley in the first half, while Ross McCormack and Michael Brown had earlier gone close to breaking the deadlock.
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