The man Jürgen Klopp once termed the king of cup competitions is yet to live up to his reputation in that department since revolutionising Aston Villa, with Everton advancing to the fourth round of the Carabao Cup at the expense of Unai Emery’s side courtesy of goals by James Garner and Dominic Calvert-Lewin. The Villa substitute Boubacar Kamara pulled a goal back late on but Everton held on through five minutes of nervy second-half stoppage time. Emery’s track record as a serial cup winner on the continent cannot be disputed but since arriving at Villa last November it has been a different story. At the beginning of this year Villa suffered a sorry FA Cup third-round defeat at home to Stevenage, then of League Two, and last week their return to European group-stage action did not go to plan in Warsaw. His second game in charge was a defeat to Manchester United at the same stage of this competition last season. The last time these sides met, here in the Premier League last month, Villa wiped the floor with their opponent, winning 4-0. It was not exactly a case of role-reversal but from the moment Youri Tielemans sent a dipping shot on to the roof of Jordan Pickford’s net on eight minutes Everton were far superior. Pau Torres was nervy in possession and Robin Olsen, who deputised for Emiliano Martínez, unconvincing. Olsen’s poor kick led to Everton taking the lead on 15 minutes, with Calvert-Lewin and Arnaut Danjuma playing head tennis before Amadou Onana located Garner with a fine reverse pass. Garner controlled the ball with his right foot, took another touch on his left to compose himself and then wellied the ball in at Olsen’s near post. Cue a wall of noise from more than 4,000 Everton fans stationed in the North Stand, normally home to Villa fans. Calvert-Lewin was jeered off on his last visit to Villa Park in August and Michael Keane, who endured a nightmarish afternoon, has not started a league game since. Seven of that lineup also started here but Everton were a different beast under the lights. Jack Harrison was brilliant on debut, harrying Torres at every opportunity and he superbly freed Calvert-Lewin towards the end of the first half. Calvert-Lewin read the sumptuous pass but shot at Olsen and then hit the rebound, albeit from an acute angle, against the side netting. That Emery made a triple substitution at half-time spoke volumes. Lucas Digne, Kamara and Ollie Watkins, all of whom will likely returning to the starting XI at home to Brighton on Saturday, entered. Until Digne’s arrival, the captain John McGinn operated as an unorthodox left-back, with Àlex Moreno unavailable because of a hamstring problem. Everton, meanwhile, were invigorated by the five changes from victory at Brentford, none more so than Harrison. Surely Villa could not play much worse? Five minutes into the second half they trailed by two goals. Tielemans sold Ezri Konsa short and Calvert-Lewin pounced on the ball and burst forward and, with only Olsen to beat, coolly finished. Two minutes later Pickford made a smart save to deny Moussa Diaby after Watkins powered forward but until Kamara’s deflected 83rd-minute strike, which ensured a grandstand finish, Everton were unusually comfortable. “The thing is the story of Everton has been a two or three-season thing with a cloud hanging over [the club],” the Everton manager Sean Dyche said. “The only way to change the story is us.”