Nikica Jelavić’s sixth-minute free-kick was handled by Fulham striker Pavel Pogrebnyak, and the Everton striker duly put the home side ahead from the spot.
Marouane Fellaini then headed Steven Pienaar’s corner past Mark Schwarzer to double the Toffees’ lead, before Jelavić added his second with a close-range finish five minutes before half-time.
Moyes’ side then wrapped an emphatic win in the 60th minute when Pienaar’s chipped pass released Toffees captain Tim Cahill, who poked his finish under Schwarzer.
Everton’s victory leaves them in seventh place, two points clear of Merseyside rivals Liverpool, prompting Moyes to pay credit to his January signings for turning around the Toffees’ ailing season.
“Steven Pienaar’s performances have given us the creativity, Nikica Jelavić has given us the goals, and Darron Gibson has given us a little bit of stability,” said Moyes.
“I think all those things have been a big help.”
He added: “I thought on Saturday, people like Leon Osman, Phil Neville, Tony Hibbert did well.
“There were a lot of really good performances. I was able to enjoy the game because the players had got us a couple of goals up and we were playing with a really good style.”
Everton have an outside chance of qualifying for the Europa League but face a tricky trip to the Britannia Stadium to take on Stoke City before their final game of the season against relegated Wolverhampton Wanderers.
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