But a combination a David Marshall and the woodwork kept the Foxes out during the first half.
The pressure from the home side was less intense in the second half and City, with Bellamy's pace, were always dangerous on the break.
The victory completes the first half of the season with Cardiff playing all 23 of the other teams in the League and it's Cardiff who lead the table.
At the time of writing Crystal Palace are playing at home against Hiddersfield. A win for Palace would see them into second place.
Elsewhere Middlesbrough lost at Leeds and Millwall lost at home to Barnsley.
Cardiff's Christmas fixtures continue with Palace at CCS on Wednesday and Millwall at CCS on Satuday. Both 3:00pm kick offs.