Palace extended their unbeaten home run to eleven games as KG's goal proved enough to overcome a stubborn Cardiff side and move the Eagles four points clear of the relegation zone.
Julian Speroni returned to the starting line-up as Dougie Freedman made just one change from the side that narrowly lost at Turf Moor on Saturday.
James Vaughan was the first player to test a keeper, with a header from a David Wright cross, but his effort went straight at Stephen Bywater. Wright was causing problems in midfield, as a creator rather than a destroyer and after a lovely Palace move involving Danns, Ambrose and Iversen, his brilliant chipped through ball found Vaughan. The on-loan striker controlling the ball perfectly on his chest but slipping as he went to apply the finish.
Then a slip from Dekel Keinan after a long Dean Moxey clearance almost let in Palace's top scorer but the chance wouldn't come down for Vaughan as he went through on goal. Palace continued to pour on the pressure and good strength from Iversen in the box almost led to a chance for Neil Danns
A KG cross then found Vaughan, who seemed everywhere but his header dropped just wide as Palace had the best of the first 20 minutes. Nearly 30 minutes went by before Jay Emmanuel Thomas became the first Cardiff player to test Speroni, but his shot was easily gathered.
As the half drew to a close, Palace looked to make their pressure tell with a goal and Neil Danns had perhaps the best opportunity but could only drive his shot wide after great work from Vaughan and a clever Iversen touch.
Cardiff came out of the blocks in the second half on fire but Palace's defence held firm with relative ease forcing the visitors to shoot from distance. First Emmanuel-Thomas let fly and Speroni did brilliantly to touch the ball onto the crossbar and behind, and then Stephen McPhail let rip another 30 yard drive, which was also tipped over.
Suddenly Cardiff were on top and a free-kick from the left caused havoc with Dekel Keinan rising highest to head against the upright. The rebound fell to Michael Chopra whose goalbound effort hit David Wright's outstretched arm and the referee pointed to the spot. Up stepped Peter Whittingham, only to see his shot rebound off the right hand post as Palace breathed again.
Palace, boosted by the miss, hit back immediately and a Neil Danns shot was only parried for James Vaughan to tap home. Up went the flag though and despite Palace's protests the goal was disallowed.
Minutes later the Eagles did get the rub of the green though when Pablo Counago's throughball was almost cleared by Keinan only for the ball to hit KG on the heel, and dribble into the corner for 1-0.
With less than ten minutes left Dougie Freedman threw on Claude Davis to protect the lead and although Jay Bothroyd went close with a header and had a goal disallowed for offside, Palace held on for a seventh win in eleven games at Selhurst.
Crystal Palace: 1. Julian Speroni, 2. Nathaniel Clyne, 3. David Wright, 5. Patrick McCarthy (c), 7. Darren Ambrose (Claude Davis '85), 8. Neil Danns, 9. Steffen Iversen (Pablo Counago '69), 20. James Vaughan (Sean Scannell '89), 29. Dean Moxey, 31. Anthony Gardner, 34. Kagisho Dikgacoi
Subs Not Used: 13. Lewis Price, 10. Owen Garvan, 16. Wilfried Zaha, 19. Jermaine Easter
Bookings: McCarthy, Dikgacoi
Cardiff: 42. Stephen Bywater, 2. Kevin McNaughton, 5. Mark Hudson, 7. Peter Whittingham, 8. Michael Chopra (Chris Burke '80), 9. Jay Bothroyd, 10. Stephen McPhail, 12. Dekel Keinan, 14. Paul Quinn, 25. Jay Emmanuel-Thomas (Jon Parkin '84), 39. Craig Bellamy (c)
Subs Not Used: 13. Jason Brown, 4. Gavin Rae, 6. Gabor Gyepes, 23. Darcy Blake, 27. Adam Matthews
Att: 12,549 (1,015) Ref: Mr M Russell