Yakubu's second goal since his arrival on loan from Premier League side Everton and King's fourth goal in his last three league games gave the Foxes a vital three points as they moved up to seventh place.
Sven-Goran Eriksson's side's push for the play-offs continues to gather pace after their fourth successive win leaves them unbeaten in seven league games.
The home defeat for Derby piles more pressure on boss Nigel Clough and leaves the Rams languishing in 17th place in the table, without a win in six league games.
Source: PA
Source: PA