Belgian international Romelu Lukaku had opened the scoring for the hosts with his 50th for the club.
Ross Barkley's excellent goal sealed an impressive 2-0 win for Everton over West Ham in their Premier League clash on Sunday ending a four match winless run in the league.
For Barkley -- who had been dropped both from the England squad and the Everton starting line-up this season as his form dipped -- it was his first goal since the opening day of the season against Spurs.
Belgian international Romelu Lukaku -- who set up 22-year-old Barkley for his goal -- had opened the scoring for the hosts with his 50th for the club.
It also maintained his extraordinary record against the Hammers as it was his ninth goal in as many Premier League matches against them since he moved to Everton.
Everton stay sixth, just five points off the top trio of Manchester City, Arsenal and Liverpool -- West Ham stay firmly in the bottom half of the table three points above the relegation places.
Everton manager Ronald Koeman said he was pleased with Barkley's performance but added he needed to be more aware on the pitch of what was required of him.
"It was a total team performance today," the Dutchman told Sky Sports.
"Ross Barkley had more impact in the last part of our attacking, not only in scoring but he was dangerous throughout.
"That's what the team needs. He can be very good, but it is all about knowing what you need to do. Sometimes I have to shout too much, he needs to run more."
West Ham should have gone one-up in the 12th minute as a deft pass by Dimitri Payet slipped Pedro Obiang free in the box but he completely miscued his shot as it ballooned over the bar.
The hosts produced some sparkling attacking football after the early West Ham forays into their own half none more so than when Costa Rican Bryan Oviedo nipped in to win a ball that the West Ham defence should have dealt with.
He looked up and found Barkley free in the box but his goalbound effort was brilliantly turned away by goalkeeper Adrian.
Gueye, though, showed less alertness in defence as he had to resort to tugging at Obaing's shirt bringing him to the ground and earning himself a booking which rules him out of next weekend's clash with Chelsea.
The hosts took the lead five minutes into the second-half as Winston Reid's poor clearance was played back into the Hammers box.
Yet again the extra hunger of the Everton players played a decisive role as Yannick Bolasie charged into the area and got to the ball ahead of Reid after Adrian had saved Seamus Coleman's shot -- his perfectly delivered cross was headed into the empty net by Lukaku.
Robles then produced a spectacular diving save to deny Mark Noble as West Ham turned on the pressure searching for the equaliser.
That was as good as it got for West Ham as Barkley's magic produced the decisive second goal 15 minutes from time.
The England international gained possession looked up and saw Lukaku breaking free down the right and found him with a perfect long pass.
The Belgian dallied long enough for Barkley to make up the ground and then produced the perfect cross for the midfielder to beat Adrian with a half volley, celebrating by beating his chest and tugging at his shirt in answer to his critics.