Chelsea have returned from the international break with a spirit, authority and resilience that bodes well for Xabi Alonso. His problems at Everton, not a happy hunting ground in recent years, were limited to the seven minutes Emi Martínez needed treatment for a head injury as Pedro Neto’s brace gave him a deserved victory in the Merseyside sun. The Argentine goalkeeper was taken to hospital for tests after an accidental collision with Jarrad Branthwaite which left him with a suspected concussion. “When he left the stadium he was conscious,” Alonso said. “Hopefully it’s not so bad, but we have to wait.” A first Premier League clean sheet since January, and a second successive win since losing at Brentford before the Nations League break, were achieved with a minimum of fuss in a commanding second-half performance. “It’s a day,” the Chelsea boss responded when asked if the victory, built on a feisty first-half display and a mature second half, provided evidence of the mentality he craves at Stamford Bridge. “We need to repeat it again and again to be sure, but the mentality was very good. Sometimes it’s not about playing well, but about playing good football, winning a lot of second balls and being efficient. We need a game like this. The feeling in Brentford was that it wasn’t enough. Today was better, but it’s just one. When it’s 10 clean sheets…”There were goalkeeping problems at both ends of the pitch, with Jordan Pickford unconvincing for the second week in a row for Everton. David Moyes’ side cruised through the first half and could have legitimate complaints about Morgan Rogers avoiding a second yellow card moments before half-time. But from Pickford’s feeble attempt to stop Neto’s first goal to Thierno Barry missing his only big chance of the game, there were self-inflicted wounds in Everton’s first defeat of the season. “It’s not that we played that badly overall,” Moyes said. “We just didn’t create enough, which meant if we did something wrong defensively, it would count against us.” That’s how it turned out. There was more needle than quality in the first half and Rogers, already cautioned, was very lucky to avoid a second yellow card from the referee, Paul Tierney, by launching into a challenge with James Garner. The Chelsea striker caught the ball and the man. The tackle could be considered as reckless as the one that led to an earlier booking for Harrison Armstrong. Barry wasted Everton’s best chance by heading Jack Grealish’s cross straight at Martinez from close range. Another big error from Barry was one of several recurring themes that undermined Everton’s afternoon. Pedro Neto shows his joy after giving Chelsea the lead. Photograph: Molly Darlington/Getty Images Chelsea began to hold off the hosts and turn the tide as half-time approached. They were inches away from taking the lead in spectacular fashion. Moisés Caicedo moved towards the far post for a Jordan Henderson corner that landed exactly where the training ground routine required it. His thunderous volley went over Pickford but hit the crossbar, leaving him shaking for several seconds. Skip Beyond Newsletter Promotion Free Newsletter | Every weekday Subscribe to Football Daily Start your evenings with The Guardian’s take on the world of football after the newsletter promotion Neto forced a decent save from Everton’s goalkeeper from distance in first-half stoppage time and beat him from a much closer range 44 seconds after the restart. As in the draw at Hull last weekend, Ainsley Maitland-Niles and Pickford had defensive shortcomings. Rogers was inevitably involved when he released Jorrel Hato, Alonso’s only forced substitution since Bournemouth’s 5-1 defeat, away from Maitland-Niles on the Chelsea left. Hato’s cross had a lucky touch from James Tarkowski on its way to Neto, whose shot beat Pickford’s weak attempt to save low to his left. The goalkeepers’ concerns took on a much more serious character when Branthwaite collided with Martinez while challenging a Kiernan Dewsbury-Hall free-kick. The Chelsea goalkeeper needed a lengthy treatment before being carried away with a neck brace and the uncomfortable sound of Everton’s boos. Fortunately, he gave Branthwaite a thumbs up as the concerned Everton defender waited to wish him well. Martinez’s replacement, Mike Penders on his Premier League debut, was not seriously tested as Everton’s threat faded and Chelsea remained in control of the second half. Victory was sealed in the final minute of normal time when Henderson’s free kick hit Barry’s head, bounced off Everton substitute Tyrique George and Vitalii Mykolenko, before falling to Neto. The Chelsea winger finished with confidence after Pickford’s desperate attempt into the bottom corner.