After an unimpressive first half display, the Nigerian headed home from six yards off Willian's whipped free-kick to break the deadlock in the 66th minutes of the with only his fourth Blues goal.
Mikel got the starter’s shirt despite Jose Mourinho’s changes to the squad that won Southampton 3-0 on New Year Day.
Even though it was another more prolific African Samuel Eto’o who was expected to deliver the goals for the Blues, Chelsea’s curtain raiser came off the boots of the unlikely Mikel.
Oscar then doubled Chelsea's lead four minutes later with a powerful strike from the edge of the penalty area that Derby goalkeeper Lee Grant was unable to keep out.
Mikel had earlier broken his 261-game goal drought in the English Premier League in Chelsea’s 2-0 victory over Fulham at Stamford Bridge on September 21, 2013.
Chelsea will now face Stoke City in the fourth round of the oldest knock-out competition in English football history.