The win over Crystal Palace was the end of a three-game losing streak.
Dominic Calvert-Lewin put the hosts in front after a brilliant turn inside the box in the 11th minute.
Anthony Gordon tapped in a rebound to make it 2-0 after the break - although it was initially ruled out for an obstruction before being reviewed by the VAR - and substitute Dwight McNeil added a third late on.
Palace came close to scoring in the second half through Michael Olise, who had several chances.
Palace, who have come from behind in all three of their victories this season, never really got a strong foothold on the game.
The type of ruthlessness thatLampard has called for in recent weeks was shown byEverton.
The Blues moved up to 11th place, level with Palace, who dropped to 12th.
It was a step in the right direction as he continues his rebuild following a near-relegation last season and a win over Palace in May.
He called for his side to show more bravery and to have more of a clinical edge in the box.
They pressed high and intensely, forcing Palace to make mistakes at the back and pushing them deep into their own half.
In the middle of the field, Amadou Onana broke up play and switched possession effectively, while Gordon was busy on the right side.
It was that side of the pitch where the opening goal was scored.
The Palace skipper lost possession and when Alex Iwobi floated it into the path of Dominic Calvert-Lewin, he did the rest with a clinical finish in front of the England boss.
When he came off in the second half, he was given a standing ovation because of the impact he had on the game.
Despite being frustrated on a number of occasions,Everton were in control throughout and the third goal capped off an impressive performance, as Iwobi's backheel set up substitute McNeil to fire in from close range.
Palace grew into the game in the second half and saw more of the ball than they did in the first.
It was Gueye who lost possession on a couple of occasions, but Wilfried and Eberechi were not able to take advantage.
Olise's flick was inches over the bar after he was picked out at the near post.
Olise and Zaha were tested by the defence but they held firm, while Andersen had his work cut out for him.
Even though Palace were physical, they stood up to the challenge, even when emotions got the better of them after a tackle from Gordon.
It was a frustrating afternoon for Patrick Vieira's side, who had gone three games without a defeat before heading to Goodison Park.
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