Speaking on the Andrew Marr Show, the prince explained that he refused to travel to the US "15-love" down to the Americans and so came up with his own way to one-up them: getting his grandmother involved.
He said: "She was more than happy to oblige."
He added that she was "highly competitive".
The prince said that he could think of no one else who could top the President and First Lady of the United States.
He said that he thought to himself: "This has to be the Queen, otherwise we lose."
The Queen appeared alongside her grandson in a video for the Invictus Games last month.
She and Harry could be seen viewing a video message from the Obamas and their staff in which the couple warned that the US would be bringing their A-game to the tournament.
Her Majesty could be seen smiling wryly and laughing "Oh really, please!", before Prince Harry carried out his own mic drop.
Harry also told Marr about the "incessant" intrusion into his private life.
He said he was trying to negotiate a private life where "if I talk to a girl, that person is then suddenly my wife, and people go knocking on her door".
"Everyone has a right to privacy," he said.
"Sadly, that line between public and private life is almost non-existent any more."
Harry will attend the opening ceremony of the Invictus Games today, joining US first lady Michelle Obama at the event.
The launch show, featuring British acts James Blunt and soprano Laura Wright, will also see Hollywood star Morgan Freeman perform.
Harry has spoken about his hopes for the "amazing" tournament and acknowledged the pressure of maintaining the event's legacy.
The 31-year-old royal said he may have set the bar too high with the inaugural games staged in London in 2014, but after touring the Florida venues on Friday and chatting to competitors, he declared the sporting facilities in Orlando "awesome".
Harry has been the driving force behind the Paralympic-style event for injured servicemen and women and veterans and over the five-day tournament more than 500 athletes from 14 countries will compete in a range of sports.
The Prince told the Press Association: "It's going to be amazing, the atmosphere is going to be incredible.
"There's still a few more tickets to sell but we're just inviting people to come down and enjoy what's going to happen, it's going to be fantastic.
"Speaking to all the competitors, they're very happy, the food's great - which is what they care about - the accommodation is excellent. Once they're over the jet-lag they just want to get going."
The first medals were presented yesterday by Harry but the tournament where sportsmen and women from countries like Italy, Germany, Australia, Estonia, Jordan and the UK will compete will begin in earnest tomorrow.
During the day Former US president George Bush will present a symposium about the "invisible wounds" of war, like post traumatic stress, and the prince will join him at the start of the day-long event held before the Invictus opening ceremony.