Chelsea transfer target Anthony Gordon had put Frank Lampard’s side ahead after 24 minutes amid yet more uncertainty over his future.
Everton, with just a point to their name from their opening three fixtures, had looked decidedly shaky at the back in the opening stages but took the lead after 24 minutes with a simple goal.
Coady launched a long ball over a static defence and 21-year-old Gordon, who could move to Chelsea for around 60 million pounds in the next few days, took a touch to bring it down and then steered it calmly past David Reya.
Either side of that Brentford twice hit the post via a Mathias Jensen shot and an Ivan Toney header, with Yoane Wissa somehow volleying the rebound horribly over the bar.
Brentford, who hammered Manchester United 4-0 in their last home game, took total control in the second half as Christian Norgaard hit the bar and Jordan Pickford made some sharp saves and they eventually got the breakthrough when Keane Lewis-Potter flicked on a corner for fellow substitute Janelt to knock in from close range six minutes from time.