A further chance fell the Bluebirds' way when Taylor headed towards goal, but Steve Sidwell was able to prevent it from crossing the line.
Aron Gunnarsson was next to threaten for the away side with a header that rolled wide. Again Whittingham was the architect.
However, Fulham equalised just before the break through Bryan Ruiz's chipped shot.
Cardiff's Whittingham, for so long the maker of chances, then had one of this own with a volley, but drilled it wide.
It should have been 2-1 to the Bluebirds moments later when Frazier Campbell beat Hangeland inside the box, but he fired over.
It was a similar story at the other end, with Berbatov heading wide at the near post, while Ruiz failed to make the most of a decent attacking position.
However, with the match heading for a draw, Mutch arrowed the ball into the net.