It was the only major upset on a night where Leicester continued their recovery to advance with Bournemouth, who sent Everton 4-1 down in a Premier League game.
Damsgaard, who impressed for Denmark at the European Championship last year as a replacement for Christian Eriksen following his cardiac arrest, received his World Cup call-up in Qatar on Monday night.
A day later he showed his skills with a neat touch and pass for Ivan Toney to open the scoring in the third minute for Brentford, who dominated the game but failed to put their chances aside.
Gillingham, who – in second-to-bottom place in League Two – are 77 places below Brentford in the English football pyramid, scored with their only goal attempt in the game through Mikael Mandron in the 75th to lead it to the shoot to the net.
After the first 11 attempts were converted, Damsgaard missed and Gillingham reached the last 16 for only the second time in their history.
Toney sent a message to England manager Gareth Southgate – and possibly some of his own critics too – with his ninth goal of the season, which he celebrated by putting a finger in each of his ears.
The striker took to social media over the weekend to say he was helping the English Football Association with an investigation. It came after a report in Britain’s The Sun newspaper said he was being investigated over match betting allegations relating to a period before he joined Brentford.
Brentford acknowledged he was aware of the story but would not comment further.
In his Twitter post, Toney described himself as a “proud Englishman” who dreamed as a child of playing for his country at a World Cup. He is one of a host of forwards looking to make Southgate’s 26-man squad – to be announced on Thursday – as a replacement for captain Harry Kane, and his cup goal was a final boost to the English coach.
Toney was called up by England for the first time ahead of Nations League games against Italy and Germany in September but did not play a minute in either game.
In form, James Justin looked to have put himself in an injury cover position for both full-back positions in England’s World Cup squad.
Justin was carried off in the second half of Leicester’s 3-0 win over Newport County following an innocuous challenge. The World Cup starts in 12 days.
Justin had scored the opener against Newport, the fourth-tier side who beat Leicester in the FA Cup in 2019 to help end Claude Puel’s reign and usher in Brendan Rodgers’ current tenure at the club.
Jamie Vardy, something of a forgotten man at Leicester, added the other two goals.
Everton’s form has plummeted as the English football club head into a six-week World Cup break.
With the heavy defeat at Bournemouth, Everton have won just one of their last seven games in all competitions to put pressure on manager Frank Lampard, whose side sit fifth to bottom in the Premier League. .
Lampard fielded a virtual reserve team and paid the price for it as Jamal Lowe’s deflected shot and Junior Stanislas’ close-range finish put Bournemouth 2-0 ahead.
Demarai Gray reduced the deficit before late goals from Emiliano Marcondes and Jaidon Anthony for the hosts.
The third round continues on Wednesday, when Liverpool begin their title defense with a home game against third-tier Derby County and Manchester City host Chelsea in the showpiece of the round.
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