Everton 3 Fulham 0: Sigurdsson, Tosun end winless run
Second-half goals from Gylfi Sigurdsson and Cenk Tosun secured only a second victory of the league season for the Toffees and ended a run of back-to-back defeats.
The win, which leaves Fulham three points outside the relegation zone, extended Everton's record run of wins at home against Slavisa Jokanovic's side to 22.
Fulham's bright start was not affected by the loss of Timothy Fosu-Mensah to a serious-looking injury eight minutes in, and Andre Schurrle wasted a great chance to put the visitors ahead when he blazed over the bar after being teed up by Ryan Sessegnon.
There was another huge let-off for Everton before half-time, with Sessegnon finding only the crossbar after being picked out in space in the penalty area by Jean Michael Seri.
Frustrations had been building in the Goodison Park stands and they grew among the home fans seven minutes into the second half, when Sigurdsson smacked the bar from 12 yards after Denis Odoi was penalised for a push on Dominic Calvert-Lewin.
Sigurdsson made amends three minutes later, though. Having released Jonjoe Kenny down the right with a clever pass, the midfielder followed up to intercept a poor clearance and curled a first-time finish into the bottom-left corner with his left foot.
Luciano Vietto's heavy touch saw Fulham miss the chance to equalise, and the miss was punished 66 minutes in when substitute Tosun nodded home Theo Walcott's cross from the right.
Sigurdsson netted his second on the break in the closing stages with a composed side-foot finish, via a slight deflection, to seal Everton's first league win since they beat Southampton on August 18.
18 - Since 2011/12, Gylfi Sigurdsson has netted 18 goals from outside the box in the Premier League, a haul only Philippe Coutinho can better (19). Range.
— OptaJoe (@OptaJoe) September 29, 2018
What it means: Everton closing on Manchester United
Everton's first win in the league since August means they are now on nine points from seven games, just one behind Manchester United, who lost 3-1 at West Ham earlier on Saturday.
It is only their second top-flight win under Silva, but their improved display in the second half will come as a particular sign of encouragement on Merseyside.
Fulham, for all their enterprising play, sit just three points above the drop zone after claiming only one win and two draws from their first seven games back in the Premier League.
Sigurdsson stepping up as Everton's key cog
Sigurdsson's Everton career has not been a resounding success, but this was a performance that suggested a growing confidence within the Iceland star.
Having missed his penalty, Sigurdsson wasted no time in making things right, inspiring the move that led to his exceptional finish to put Everton 1-0 ahead. He capped a strong all-round showing with a deflected late strike.
| What. A. View. #EFCMatchday pic.twitter.com/gSOsE1JkWd
— Everton (@Everton) September 29, 2018
A damning day for Odoi
Fulham's defending was largely based on frustrating Everton's forwards with physical challenges and quick pressing, but Odoi took matters too far.
His high challenge on Richarlison should really have been punished with a card, and his careless shove on Calvert-Lewin gifted Everton their penalty. Okay, Sigurdsson missed, but Odoi should not escape criticism given he then allowed Tosun a free header to score the hosts' second.
What's next?
Everton are in EFL Cup action against Southampton at Goodison on Tuesday, before they resume league duties with a trip to Leicester City four days later.
Fulham have eight days to prepare for the visit of London rivals Arsenal, who won their first two away league games of the season.