Second-half goals from the midfield pair proved enough to settle a timid west London derby after Jose Mourinho had left out Juan Mata and David Luiz from his 18-man squad
The Blues end their run of four games without a win by beating the Cottagers, but Jose Mourinho's side looked out of sorts during large periods of the game.
Chelsea entered the match without a victory in its last four matches in all competitions, and could have trailed in the early stages when Fulham striker Darren Bent was presented with a terrific chance.
Bent wasted his effort though, and after a scrappy first half, the Blues took the lead through Oscar's close-range finish in the 52nd minute.
Mikel subsequently capped off the victory with his first Premier League goal – plundered during his 185th appearance – when he hooked in following yet another Chelsea corner.
Mourinho reacted to his side's 2-1 home defeat to FC Basel in the Champions League on Wednesday by swinging the axe, making four changes, as Juan Mata and David Luiz were left out of the squad while Frank Lampard dropped to the bench.
Captain John Terry was recalled by Mourinho, as were Mikel, Ramires, and attacker Andre Schurrle.
Fulham made three changes of their own, with Damien Duff - one of three-ex Chelsea players in their starting side.
The visitors fashioned the first chance of the match when Steve Sidwell, another former Chelsea player, headed over, and although Samuel Eto'o flicked wide at the other end, the visitors should have taken the lead in the 13th minute.
A superb pass from Pajtim Kasami set Bent free, but the Aston Villa loanee – who entered the match with three goals in his last three matches against Chelsea – failed to make the most of the one-on-one opportunity, shooting straight at goalkeeper Petr Cech.
Chelsea's abundance of possession, and several set-pieces, failed to materialize into anything substantial, with further half-chances for Eto'o and a hopeful Hazard volley the best it could muster before Branislav Ivanovic saw a good drive turned wide by Fulham goalkeeper David Stockdale on the stroke of halftime.
Chelsea got its goal seven minutes after play resumed, however, as Oscar found himself in the right place at the right time.
Schurrle was the instigator, skipping past Reither before shooting from the left with an effort that was spilled by Stockdale.
Fulham panicked and failed to clear its lines properly and Oscar was on hand to tap in with his left foot, much to the delight of the home supporters.
Sidwell had a good chance to level proceedings less than two minutes later, but could not direct his header on target, while Hazard went close at the other end.
Stockdale then made a terrific save to deny a thumping Fernando Torres header, but from the resultant corner Chelsea scored again, as Mikel pounced on Terry's header to thrash home a landmark goal with just six minutes to play.
And despite Kieran Richardson forcing Cech into a smart save late on, Chelsea held on for an important three points, as it extended its unbeaten record against Fulham in the Premier League to 15 matches.