Everton produced another commanding performance at Goodison Park on Saturday afternoon but fell to a 1-0 defeat against Wolves.
Despite enjoying the best of the goalmouth action, a late headed effort from Wolves second-half substitute Sasa Kalajdzic saw the away side steal the victory.
Dyche made three changes from the starting line-up at Aston Villa, with summer recruit Arnaut Danjuma plus prospects Lewis Dobbin and Jarrad Branthwaite all making their first starts of the new Premier League season.
It was one of the fresh faces who had Everton's first chance of note inside five minutes when good pressure from the Blues' front line forced a turnover deep inside the Wolves half. Danjuma collected the free ball, turned and fired a strike towards goal but he couldn’t keep it under José Sá’s net.
He was in the thick of the early goalmouth action again minutes later as he broke free inside the six-yard box to try to meet a curled Nathan Patterson cross but couldn’t get enough on the header to direct it at goal.
The Blues kept piling on the pressure with Danjuma again in the thick of the action. As the game approached the quarter-hour mark, he met a pass from Onana, threaded through the heart of the Wolves' defence to go one-against-one with Sá, but the shot-stopper managed to fingertip his effort onto the post.
Everton continued to dominate the early stages and, following an impeccable tribute in the 26th minute for Michael Jones, nearly broke the deadlock. From a corner, Garner collected a loose ball and fired a vicious effort at goal. The ball deflected off Dobbin and forced a good save from Sá who then parried it away into the path of Tarkowski, but the defender’s shot was sliced into the side netting.
Another chance went begging 10 minutes before the break when Patterson found Danjuma with a deep cross into the box, but his low volley rolled agonisingly wide of Sá’s left post.
The Blues went into the half the better side and without having conceded a single shot on target, but the scores remained level.
It was another ferocious start from the Blues for the second half, and Branthwaite was first to test Sá after just eight minutes when he reacted first to a Garner deflected shot but his header was straight into the arms of the grateful Wolves goalkeeper.
The Blues got a scare as the game approached the hour-mark, Wolves’ Fabio Silva put the ball in the back of Pickford’s net but was immediately flagged for offside.
That chance sparked some life into the away side for the first time, and they were denied an unwarranted lead by a phenomenal save from Pickford who got down excellently to palm a deflected Branthwaite touch from close range.
Chermiti joined the action for Dobbin as Dyche tried to find the formula for the elusive breakthrough, but the goalmouth agony continued for Everton. This time, Doucoure’s diving header was tipped over the bar by an outstretched Sá who refused to give up his clean sheet.
Doucoure was denied again with 10 minutes to go, this time he did put the ball in the back of the Wolves net, but a tight offside call went against him.
Then, with just four minutes of normal time remaining, Wolves’ first shot on target handed them the lead as Kalajdzic glanced a deep cross past Pickford.
Keane and Cannon joined the action late on as Everton fought for a response, but the visitors held on for the win.