With Spanish playmaker Juan Mata not deemed worthy of a place in the Blues squad, there was precious little guile about the home side's attacks, with Eto'o largely ineffective before being replaced by Fernando Torres in the second half.
Mourinho says Juan Mata must adapt to return
Chelsea were, nonetheless, deserving winners against a Fulham side that tired in the final half hour and have now not won a match since the first game of the season.
The visitors had held their own in the first half and should have taken the lead when Bent was played through on goal by Pajtim Kasami, only to side-foot his shot tamely at Cech.
Although they dominated possession, Chelsea's play lacked imagination and energy. Eto'o twice failed to make decisive contact with Branislav Ivanovic crosses, while Eden Hazard was restricted to speculative efforts from long-range.
On the stroke of half-time, Ivanovic found space for a low shot from the right, which was saved by Fulham keeper David Stockdale with his legs.
With the tension growing in the stands, Oscar delivered the breakthrough the home fans were craving seven minutes after the break.
No outfield player has made more appearances in the Premier League before scoring their first goal than John Obi Mikel.
When David Stockdale failed to hold on to efforts from Andre Schurrle and Eto'o, the Brazilian was on hand to pass the ball into the net from inside the six-yard box.
Fulham came close to an equaliser shortly afterwards when a Kasami free-kick drifted over a crowd of players to Steve Sidwell, who could not direct his far-post header on target.
From then on, the Blues were dominant. They had a penalty appeal turned down by referee Andre Marriner when Ramires went down under a challenge from Fernando Amorebieta before Torres was denied a first league goal of the season when Stockdale tipped his header over the bar.
From the resulting corner, captain John Terry rose highest to nod across goal and the ball bounced up for unlikely goalscorer Mikel to lash home.
Fulham manager Martin Jol:
Fulham must find a way to win - Jol
"The first 50 minutes they were really worried. They couldn't find the space, they couldn't find a solution and that is probably the moment you have to punish them and we couldn't do that.
"The second half they stepped up a gear, they were more aggressive than us and that is what showed.
"If you play the way we played, you have to create more. We will in the future. We needed a little bit more.
"We need a win to get back to the top 10. We're 17th or 18th, we have to get out of there."
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