The “union has worked”, according to Defence Secretary Ben Wallace, and the case for leaving will "unpick" if there was another referendum campaign.
Cabinet office minister Michael Gove insisted the "four nations" approach to pandemic has been behind the UK's successful vaccine programme and will drive the recovery from the pandemic.
Their intervention came after 20 polls in a row show that a majority of Scots now support independence and the Scottish Government says a pro-independence majority in May's Holyrood vote will be a mandate for another referendum.
"The debate around independence has always fluctuated," Mr Wallace told BBC Scotland's Sunday show today.
"But when it comes down to no longer playing the man but playing the ball in a referendum campaign or sometimes in election campaigns, then what we find is that the arguments unpick and people get serious about the debate."
Polls suggest that one factor in the spike in support for independence is the lack popularity which Boris Johnson has north of the border. But Mr Wallace, a former MSP, suggested blaming leaders is an old tactic of Nationalists.
"When I started in Scottish politics it was all Thatcher's fault, then it was Tony Blair's fault, then it was even Gordon Brown's fault when he was from Fife. And now it's currently the current Prime Minister's fault. I've seen that all before
"But when you start to play the ball, as for example with the currency debate in the last referendum campaign, it all slowly falls part.
"The union, as we're seeing in a whole range of issues, comes into its fore and its strength on certain occasions and a pandemic like this where we are better together, where we are helping share each other's science, sharing each other's capacity. Listening to each other and learning is when a union proves its strength.
"The union doesn't have to prove it's strength every day of the week. But we should all be grateful whether you're in Cornwall or Aberdeenshire that the union has worked on this event."
Mr Gove said in an article for the Mail on Sunday today that the UK's vaccine roll-out has been world-leading and compared it with the "stuttering performance" in Europe where there are growing recriminations over the slow pace of vaccine programmes.
"We are all in this together," Mr Gove wrote.
"The UK Government working with the devolved administrations in Edinburgh, Cardiff and Stormont, using the historic ties we have built up over 300 years to face down the terrible threat of Covid-19. Our greatest ever peacetime team effort.
"And what we have learned along the way is the crucial part that pooling our knowledge, sharing our experiences, learning from each other and working together across the UK will also play in us building back better and stronger from the pandemic.
"Help has been given to all four nations: financial, military and medical, and our citizens have come together in kind."