Better late than never. None of the forwards in the Republic of Ireland’s squad had scored an international goal before this match, and for a long time here that statistic looked unlikely to change. But in the 85th minute of his 11th appearance for his country, David McGoldrick leapt high to send a powerful header into the net from eight yards, negating the lead that Fabian Schär had just given Switzerland.

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The Sheffield United’s striker’s goal was enough to earn a point that sustains Irish confidence that they can reach Euro 2020. The suspense is building nicely in Group D, where Mick McCarthy’s team stand top, albeit having played more matches than their main rivals. They have a tough run-in – away to Georgia and Switzerland before hosting Denmark in their last game – but McCarthy said this performance suggests his team are at their best when the going gets tough.

“We’re not the best team in the group but I’ll tell you what, you’re going to have to put our players down before they give up, and that’s a lovely trait to have,” he said of his team.

Switzerland, ranked 11th in the world, expected to close the gap in the group here by demonstrating a gulf in class between the teams. For much of the match they were indeed slicker, controlling possession and forcing the Irish to defend tigerishly.

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When the visitors managed to pick a way through that defence, they let themselves down with erratic finishing. Until, that is, a Newcastle United centre-back joined in one of their attacks in the 74th minute, arriving at the end of a lovely one-touch move to guide a low shot past Darren Randolph. That turned out to be the cue for Ireland to work up a storm. Switzerland, who let slip a 3-0 lead to draw with Denmark in an earlier group match, lost their composure and then their lead. Glen Whelan lashed a thunderous shot against the bar in the 84th minute and then, moments later, McGoldrick outjumped a defender to nod a deflected cross by James McClean into the net.

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In a sense it was fitting that Whelan and McGoldrick led the Irish fightback. The international careers of both players seemed to have run their course under Martin O’Neill but have been revived by McCarthy.

“He has always been an excellent player, certainly for me,” said McCarthy of McGoldrick, whom he once signed for Ipswich Town. “I’m delighted he got his goal. All that heading practice that [assistant manager] Terry Connor used to give him at Ipswich.”

Lansdowne Road was not full as many fans stayed away amid continuing disgust at the controversies that have beset the Football Association of Ireland in recent months. But the supporters that turned up made a mighty racket when McGoldrick scored, which McCarthy took as evidence that supporters are still happy to recognise what is good in Irish football. “When the goal went in it was like days of old,” he said. “Like Jack’s day, my day, it was fabulous. I’d like to thank the fans for that. I’ve had a lot of goodwill shown towards me [since returning as manager in November] and so have the players despite the other stuff going on. The way the lads have conducted themselves and played has helped people to believe in the team.”

There was certainly no doubting their spirit here – and that has not always been a given in recent years – but their quality looked deficient for long spells during which Switzerland controlled possession. The Irish defence, led by Shane Duffy, did well, and when they were breached, the Swiss attackers flopped. Breel Embolo, Haris Seferovic, Ricardo Rodriguez all bungled openings in the first half.

Switzerland earned their clearest chance yet with a wonderful move in the 62nd minute but Embolo slipped as he tried to finish from eight yards. When Schär stepped forward to make the breakthrough at last following a move of clockwork precision, it turned out to be the wake-up call Ireland needed.