The Blues nearly got back into the game through John Terry as he rose highest in the penalty area to head Juan Mata's corner towards goal, but his effort hit the post and went wide.
Cardiff responded and could have doubled their lead as Whittingham whipped a dangerous free kick into the penalty area and Cech had to be at full stretch to tip the ball past the post with an excellent one-hand stop.
Jose Mourinho's side got back into the game in bizarre fashion as Cardiff keeper David Marshall was robbed of the ball when bouncing it in his area by Samuel Eto'o and the striker teed up Eden Hazard, who was left with a simple finish into an empty net.
The visitors were the first to threaten after the break as Whittingham put another dangerous ball into the area that Cech cleared, but only as far as Gary Medel on the edge of the box; however, he could only fire over the bar.
Chelsea made the midfielder pay for his miss when they took the lead. Cardiff failed to clear their lines from a corner and Hazard slipped a lovely through-ball for Eto'o behind the defence to slot home past Marshall into the net for his first goal for the Blues.
However, Cardiff came back at Chelsea and Cech was needed once again to make a good save to deny a powerful shot from Kim Bo-Kyung, which spurred the Blues on to kill the game. Ramires won the ball in midfield to release Oscar and he got the London club's third with a splendid curled effort into the top corner.
Mourinho's team began to pick the visitors apart and they duly got their fourth goal of the afternoon when Hazard picked the ball up on the left, drilled a low shot towards goal and somehow the ball crept underneath Marshall into the net.