After a stop-start first half that largely disappointed, the game burst into life in the second half, the catalyst being a missed penalty by Gylfi Sigurdsson, who went on to bag a brace either side of a Tosun marker
Everton were looking to get back to winning ways in their third game in three against opposition from the capital, following reverses against West Ham and Arsenal.
Meanwhile, Fulham came to Goodison still searching for their first ever win over the Blues at the Grand Old Lady and their 300th victory in the top level of English football.
With neither side having yet recorded a clean sheet this season, another sell out crowd at Goodison arrived fully expecting to see goals.
Marco Silva was still unable to select Yerry Mina, due to an ongoing foot injury, Phil Jagielka, Seamus Coleman and Andre Gomes. Looking to get back to winning ways and boosted by a new long-term contract for England’s number one goalie, our Portuguese boss selected his starting eleven: Pickford, Digne, Zouma, Keane, Kenny, Gana Gueye, Davies (c), Sigurdsson, Walcott, Richarlison and Calvert-Lewin.
The Cottagers spent heavily in the summer transfer window and have been praised for their style of play in their return to the Premier League, and in centre forward Mitrovic, they have a proven and wily goal threat. Head coach Slavisa Jokanovic named his line-up: Bettinelli (c), Fosu-Mensah, Odoi, Ream, Bryan, Schurrle, Anguissa, Seri, Sessegnon, Mitrovic and Vietto.
In charge of proceedings was our referee, Roger East.
In bright sunshine, Everton made the first attacking foray when a good tackle by Gana Gueye released Richarlison but his eventual pass for Sigurdsson saw a weak toe poke effort off target.
An early change was forced on the visitors when Fosu-Mensah went down needing treatment and after a long delay, he was replaced by Christie.
The first real chance went the way of Fulham as Bryan found Sessegnon in space on the right and his sweet turn took him away from Kenny but his pass to set up Schurrle saw the German blaze high over the bar.
Digne floated a left wing free kick to the back post for an unmarked Zouma, but the flag went up for offside. Another good tackle by Gana Gueye again released Richarlison for a run and his deflected shot earned the games first corner.
Theo Walcott chanced his arm from 20-yards on the 18 minute mark with Bettinelli only able to parry it before his defence completed the clearance to safety.
Just before the half hour mark, Christie was yellow carded for hauling down Richarlison.
A quick, long ball from Pickford found Walcott who laid the ball off for Kenny to find Sigurdsson for an early cross from the right that earned another corner.
The best chance of the largely uneventful first half though fell to Fulham as they worked a good opening with the ball eventually landing at the feet of Sessegnon on the right of the Everton six yard box, but his high shot beat Pickford only to cannon back off the crossbar.
Half Time: 0-0
No changes by either side at half time saw Everton press early earning two quick corners that saw Richarlison hook over on a Keane header and Zouma in space head over the bar.
Everton were awarded a 51st minute penalty as DCL went down in the area trying to get on the end of a through ball, but Sigurdsson was far too casual and his spot kick hit the crossbar.
Cenk Tosun replaced the luckless DCL on 54 minutes and shortly after, Everton finally took the lead as a Kenny cross from the byeline was only half cleared and Sigurdsson made up for his penalty miss with a sweet, low, curling shot that found the bottom corner.
Everton were looking much brighter in the second half and another quick break saw Richarlison away down the left and into the box to find Sigurdsson whose shot was blocked. Tosun was into the action with a nice layoff for Richarlison but once again a deflection forced another Everton corner.
On the hour mark, a quick break by Fulham saw Schurrle on the right find Seri on the left, but Jordan Pickford earned the applause with a quick, brave save at the forwards feet.
Cairney replaced Vietto for Fulham on 63 minutes ahead of the Blues doubling their lead as a cross from the right by Walcott was met at the back post by Tosun for an easy headed finish.
Ayite for Seri on 83 and Bernard for Richarlison on 87 minutes were further changes, Richarlison earning a standing ovation for his efforts.
And Bernard was quickly and critically into the action, getting free on the right before delaying his pass into the path of Sigurdsson to coolly slot his second and the Blues third on 88 minutes.
The Icelander was then replaced to warm applause by Morgan Schneiderlin for the final moments of, in the end, a comfortable victory for the Blues and first clean sheet of the season.