Yerry Mina opened the scoring in the 31st minute, Richarlison made it two on 48 minutes and despite a penalty from Ivan Toney, Mason Holgate added a third and Andros Townsend capped things off in the first minute of second-half stoppage time.
Story of the game
Brentford could have scored early on when Everton failed to deal with a long throw. Kristoffer Ajer turned inside the penalty area and had a shot that deflected over the crossbar.
The hosts then began to create as Richarlison dragged a shot wide, and Demarai Gray fired over for before the Toffees took the lead in the 31st minute. Bees goalkeeper David Raya pushed away a shot from Andre Gomes, which gave Everton a corner. Gray delivered it from the left and Mina headed home from close range.
Richarlison and Gray continued to have chances, but couldn't convert. Brentford then nearly levelled when Ajer sent the ball back for Canos on the edge of the penalty area, but Pickford was on hand to turn it away.
Two minutes after the restart, the lead was doubled. Allan lifted the ball into the path of Richarlison and the Brazilian fired a shot past an onrushing Ray
The visitors could have pulled one back when a Canós pass released Toney in the inside right channel. He broke in to the penalty area and lashed a ball across that was just too far ahead of the arriving Mads Roerslev.
Soon after, the lead was halved. Christian Norgaard found Toney on the inside left channel and he was brought down. Stuart Atwell pointed to the spot and Toney rolled the ball to Pickford’s right as he fell to his left.
A few minutes later, the Bees were almost even. Everton cleared a corner, but Canós played it back in to space behind the home defense, but, Toney missed his kick and Pickford was able to grab it.
On 62 minutes, Everton restored their two-goal advantage. Gray delivered the corner in to a pile of bodies, it came off a Brentford head and bounced right to Holgate, who stooped to nod in from close range.
Everton put the game to bed after some nice interplay on the right, a flick from Alex Iwobi set up Townsend to shoot and he made no mistake, beating Raya to cap off a dream start for Lampard.
Man of the match: Demarai Gray
Full of energy and a danger throughout. The service wasn't always what it should have been for him, but he still put in the work and earned his standing ovation from the Goodison Park faithful.