The first game under the lights at Hill Dickinson Stadium was illuminated by Carlos Alcaraz’s eye for goal and the promise of Harrison Armstrong. Everton’s cutting edge remains a work in progress but an awkward tie against Mansfield was negotiated in straightforward fashion. Eventually.

Nigel Clough’s resolute League One team restricted their Premier League hosts for 51 minutes only for Alcaraz to ease Everton anxieties with an accomplished finish from 20 yards.

Armstrong, the 18-year-old homegrown talent who impressed on loan at Derby last season, was the provider and created a second for Beto as Everton made it two wins from two matches at their new home.

“I’ve probably played 100 of these games in my career and 99 of them were rubbish,” said David Moyes. “I thought Harrison played well, Jimmy Garner as well. We’ve got a couple of options for Harrison so we’ll decide in the next few days what to do.”

The combined appeal of a new ground and a sensible ticket pricing policy ensured the first cup tie at Hill Dickinson Stadium was a sell-out. Mansfield, also benefiting from reduced prices of £15 for adults, £10 for over 65s and £5 for under-18s, brought more than 6,000 fans to the banks of the River Mersey to contribute towards Everton’s biggest home attendance for a League Cup tie since 1987.

Unfortunately, many had problems gaining entry and kick-off was delayed by 15 minutes to “ensure all supporters have safe access” into the stadium in time, according to a statement released by Everton. The delay can be filed under teething troubles, but it had been predicted by Evertonians when highlighting numerous issues with the club’s new digital tickets on social media before the game.

On top of complaints over how the Club View section of the East Stand operated against Brighton on Sunday, complaints that Everton have acknowledged, there is work to be done on improving the match-going experience at Hill Dickinson Stadium.

Clough said: “The 15-minute delay, at a very late stage, was not ideal. But there was not much more we could have done tonight. Everybody, including the subs, did their job.”

Despite a combined history of 275 years this was the first competitive meeting between Everton and Mansfield. The noise from a raucous away section when the half-time whistle went confirmed who was the happier with a goalless first 45 minutes. Moyes selected a strong side with Jack Grealish on the left and gave required game-time to the fit-again Vitalii Mykolenko, who missed the first two Premier League games of the season with a groin injury, Dwight McNeil and Séamus Coleman. Everton were bright in patches, but only in patches.

Mansfield goalkeeper Liam Roberts made an impressive early save from Alcaraz and stopped another effort from Armstrong. Otherwise, Everton struggled to break down a disciplined League One defence. McNeil sliced over when found unmarked inside the visiting penalty area by Grealish, while the England international also skied a decent chance from Garner’s pass.

The break came at a bad time for the visitors, who had grown increasingly confident as the first half wore on. Everton came out for the second half with greater intensity and a willingness to commit more bodies forward. Mansfield came under sustained pressure, with Grealish forcing Roberts into another important save, before it finally told.

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Collecting a lay-off from the striker Thierno Barry, Armstrong showed neat footwork inside the area to keep possession before laying it back to Alcaraz. The Argentina midfielder picked his spot to perfection and swept an unstoppable finish beyond Roberts.

Everton’s new £40m signing Tyler Dibling was introduced for his debut on the hour. Beto, the Guinea-Bissau international, also came on as part of a double substitution and should have put the tie beyond Mansfield when a Michael Keane challenge broke to him on the edge of the area. The striker had time and space to finish, more than he perhaps realised, but rushed a shot straight at Roberts.

Mansfield substitute Luke Bolton threatened an equaliser when cutting across Coleman and unleashing a powerful shot that appeared destined for the net until it struck James Tarkowski and deflected over. Armstrong almost created a second goal with a defence-splitting pass to Iliman Ndiaye but the Everton substitute, tumbling under pressure, fired into the side-netting.

But Armstrong would get his second assist of the night. Garner picked out the youngster’s run behind the Mansfield defence with a beautiful ball. The midfielder squared along the face of Roberts’ goal and Beto was perfectly placed to convert.