After two stinging defeats in the Premier League, zero goals scored and seven shipped in a debilitating start to the season, Everton’s mission was clear: dispatch Doncaster Rovers from the Carabao Cup, chalk up a first win, and prepare for Bournemouth’s visit on Saturday in far better heart. They achieved this, in a scrappy performance riven with tension until Iliman Ndiaye danced through the Rovers rearguard and pinged a cute finish in off Ian Lawlor’s right post to make it 2-0 on 74 minutes. Victory was confirmed by Beto’s late strike, and was reward for Sean Dyche for fielding a strong XI including Jordan Pickford, Michael Keane and Dwight McNeil. The pleased manager said: “We played with a little more freedom in the second half. The win was a mini-step forward, I say mini as it is a cup competition. We all know the Premier League is the be all and end all so the next challenge is Saturday.” In his measured manner Dyche offered a view on the small number of fans who abused Everton players at Euston station as they boarded the train home after Saturday’s 4-0 ­hammering at Tottenham. “I’ve kept an eye on it. Enough fans in this stadium think it’s ­unacceptable – and elsewhere, too,” he said. “I’m happy that they’ve drawn the line.” This classic early-season cup meeting of top-flight giant and bottom-tier minnow had a flashpoint when Everton’s captain, Séamus Coleman, charged over to Jack Senior to inform him not to shove Jesper Lindstrøm down the Goodison Park touchline slope again. Everton were often slick in the buildup, as when Garner tapped the ball to Lindstrøm, whose run in behind splayed the red-hooped rearguard; or when manoeuvring McNeil into yards of space, though after shaping to shoot he fluffed a ­layoff to Beto, causing Dyche to wheel round to his bench in exasperation. Earlier, the vocal band of travelling support had greeted a rare sequence from their men by mirthfully chanting: “Olé!” Now, they cheered a near-miss as Grant McCann’s charges worked the ball to Senior. Drifting into an inside-right channel he let fly, causing Pickford to leap right to save. The Rovers bench were oohing and Dyche wondered why the No 23 was unmarked. It prompted the Rovers fans to taunt their counterparts with volleys of “That’s why you’re going down”, which followed the previous jibe aimed at their manager that he was to be sacked in the morning. All very pantomime and pointing to Everton’s nerviness, which was underlined by a terrible mix-up between Vitaliy Mykolenko and Pickford that handed their foes a corner. This clumsiness was streaked through the home team until Garner offered a flash of quality via a ­devilish curved cross that Beto was inches away from connecting with at point-blank range. As the opening period ebbed away, Garner, the tie’s best performer, went closest: his volley from a corner smashed off Lawlor’s left post and Rovers escaped. Jake O’Brien, in defence, Ndiaye (attack) and Tim Iroegbunam (midfield) were all given full debuts as Dyche made six changes from the humiliation at Tottenham, the same number Doncaster showed from ­Saturday’s 1-0 League Two win against Morecambe. From this on-field cast had to come an act to break the match open or penalties would decide who was to progress: Iroegbunam-McNeil did so, when the former’s goal-bound effort from outside Rovers’ area was flicked in by the latter: at least, according to the public-address announcer, who changed his initial call to give the 24-year-old the credit. At 35 and with 15 years at the club, Coleman is the soul of Everton and an emblem of their financially straitened current times. This vast experience means a cool head, too, as the full-back displayed when easing the substitute Kyle Hurst away from goal as he sought to burst in behind. Soon after the Irishman was taken off to loud appreciation, moments after Beto missed with a free header from yards out. If the centre-forward had scored home heart rates would have lowered. Instead, they rocketed when Joe Sbarra floated into Everton’s area and unleashed an effort that Pickford saved when really the England man should have been beaten. But then came Ndiaye’s sweet solo finish and Beto’s simple tap-in. McCann said: “I can be proud of the players.” He could.