There was a brief moment of embarrassment at Celtic Park when the baton containing the Queen's message refused to open for Prince Imran to release the manuscript.
Sir Chris Hoy had carried the baton to him and then tried to help open it as the Queen looked on.
Prince Imran, who said he had practised opening the baton "two or three" times, said: "I saw it on television this morning and even I laughed. It's a great comedy act."
He said he was the only one at fault.
"I had a little bit of a problem, there was a little bit of collateral damage. I cut my thumb on that wonderful piece of Scottish engineering, but it was my fault," he said at today's daily media briefing.
"I'm not sure Chris Hoy helped but all's well that ends well. I raised a laugh."
The Queen spoke of the ''shared ideals and ambitions'' of the Commonwealth when she finally delivered the message, which had travelled the world in the Games' baton relay.
She highlighted the "bonds that unite" the 71 nations and territories when she formally declared the 20th Commonwealth Games open.
In an address directed at all the athletes competing in the Games, she made special reference to the young people of the Commonwealth, saying they are entrusted with its values and future.
The message, which was kept secret until last night, circled the globe over the nine months since the Queen placed the paper inside the baton which then visited all 71 locations.
The unique hand-crafted baton, made of titanium, wood and granite, was carried by tens of thousands of people around the world during its epic 248-day tour.
It visited Asia, Oceania, Africa, North and South America, the Caribbean and Europe before returning to the UK and finally to Scotland.
Baton-bearers included top athletes and celebrities such as Sir Chris, diver Tom Daley and singer Susan Boyle.
Thousands more "local champions" also held aloft the symbol of the Glasgow Games on its journey.
Its final lap took the baton the length and breadth of Scotland for 40 days, with 4,000 bearers joining in the nation's biggest-ever relay in more than 400 communities.
Prime Minister David Cameron thanked Sir Chris for his unexpected role in helping deliver the Queen's message.
''I thought Sir Chris did brilliantly last night. Without him we probably wouldn't have got the Queen's message out of the baton," Mr Cameron said.
''He may be retired, but he still has his uses.''
Mr Cameron took in the men's track sprint qualifying on day one of the Games in Glasgow, which takes place in the velodrome named after Great Britain's most decorated Olympian, on a brief stopover before returning to Westminster business.
He is supporting all the home nations at the competition and expects it to be a big success, he said.
''I'm a firm believer that as a Cameron who lives in England with a Welsh grandmother, who's probably got a bit of Irish blood in there somewhere, I can support all the home nations,'' he said.
''I'll be back for the end of the Games, certainly, but there's quite a lot of other stuff going on right now.
''But this has been a great opening. The atmosphere is brilliant, and the organisation is a credit to everyone involved. It seems to be a very slick operation.''