After a quiet opening, Everton almost took the lead in the 14th minute when Osman came within inches of turning home Phil Jagielka's far-post header.
The midfielder, who was restored to the starting lineup for today's game, did put his side 1-0 up five minutes later, though.
Osman sold a dummy to Aaron Hughes before curling a finish into the far corner with his left foot.
© Getty Images
Gerard Deulofeu, the second Everton change, almost doubled his side's tally with a fizzing cross-cum-shot that flew just wide of the far post, and 20-year-old went close once more in the 28th minute.
Everton continued to dominate proceedings as Maarten Stekelenburg pushed away a Coleman effort from the edge of the box with 32 minutes on the clock.
Osman came close to doubling both his and Everton's tally 10 minutes before the break, but his effort flew past the post after Stekelenburg had thwarted Ross Barkley with a good save.
A minute later, Giorgos Karagounis had Fulham's best chance of the half, but the veteran midfielder lashed his effort wide from a tight angle.
Dimitar Berbatov stepped up to make the score 1-1 from the spot after Gareth Barry had brought down Kacaniklic inside the area.
© Getty Images
Everton took the lead once more five minutes later, though, as Steven Pienaar and Romelu Lukaku combined well on the left flank before the ball found its way to the onrushing Coleman, who lashed the ball home to put Everton ahead for the second time in the game.
Barry prodded home following a goalmouth scramble and substitute Mirallas put the gloss on proceedings for Everton with an injury-time goal, as the Merseyside club moved into the top four.