Eve Muirhead's world champion rink of Scots had emerged from the morning session, in which they beat the Russians 9-6, lying third and guaranteed of a tie-breaker for a last-four spot at least.
It was then confirmed by the start of their later fixture that they had definitely made it straight into the semis, due to that final session's pre-game draw shots and the average it left them with for the round-robin stage in comparison to their rivals.
When the encounter with Denmark got under way, GB had a 3-2 lead after an opening five ends in which both rinks had stolen twos, and Team Muirhead subsequently posted three in the seventh before stealing another point in the eighth to go 7-4 ahead.
Victory looked assured, but GB allowed the Danes, in possession of the hammer, to register three in the 10th, forcing an extra end that Lene Nielsen's rink stole a point from to wrap up an 8-7 triumph when Muirhead misjudged her final stone delivery.
Ending up fourth in the round-robin rankings, GB will meet unbeaten Canada in the semi-final.
Meanwhile, GB's men's curling team missed the chance to guarantee qualification through to the semi-finals of the Winter Olympics following a 7-6 defeat by Norway in Sochi.
David Murdoch's all-Scottish rink went into their penultimate round-robin match in the Ice Cube Curling Center with five wins and two defeats, knowing victory over their nearest challengers would secure a medal opportunity.
It was win or bust for Norway as GB conceded a 2-0 second-end lead to play catch-up for most of the game, levelling 6-6 with the hammer in the ninth only to lose out in the final end.
That leaves their last fixture against China possibly crucial, with Norway - who have two games remaining against Switzerland and Denmark - still a threat.
Murdoch remained defiantly optimistic, saying: -" I fancy our chances, I really do", after round-robin session 10 ended with Sweden guaranteeing their semi-final berth by beating Russia 8-4 and Canada also unable to miss out.
China are in second place with six wins and one defeat, followed by Canada, who have six wins and two defeats.
Even if the Canadians lose their last game - to the Chinese in the evening session - the worst they could finish is tied at 6-3 with Norway and Team GB, and they would qualify on a superior head-to-head record.
To add to a complicated scenario, Britain could fail to beat China and still get a play-off spot should Norway falter twice, although a win for Murdoch's men would guarantee a play-off spot at least.
The Scot admits he is going about winning an Olympic medal at the third time of asking "the hardest way possible", but remains positive.
"It is still in our own hands, we can't let that defeat affect us too much," Murdoch said.
"It is still possible. It would have been nice to get that win today and secure that play-off but you have to move on.
"We could have been more clinical today and could have been in front earlier. We had them on the ropes a little bit and never took our chances.
"Thomas Ulsrud (Norway skip) played an incredible shot with his last in end four or we were getting a handful in that end.
"But we played some good stuff in the first five and played some decent stuff in the last five as well.
"We have a good record against the Chinese team. Obviously they are playing well, but so are we.
"We have lost a couple of games only by a few inches and we need to take the positives from that."
Murdoch insists two previous Olympic disappointments have had no bearing this week.
"It is not something that you think about," he said. "You are very focused out there and you have objectives and so many other things to think about, you don't even think about past Olympic campaigns.
"That is something to reflect on at the end. We have to make sure we win tomorrow and if we do that we are still in."
Haavard Vad Petersson, who won a silver with Norway at the Vancouver Games in 2010, was delighted to leave the morning session with qualification hopes still intact.
"It was one of the most important games of our career," he said. "We had to win this one to stay alive.
"This is the Olympics, we don't want to lose. We have won a medal before but we want to get gold.
"We need probably two more wins, depending on the other games. One might do, for a tiebreaker."
The winner of the play-off will face the Swedes, who are reigning world champions and beat GB 8-4 in the round-robin stage, in the last four.
Murdoch claimed the tie-break left him with mixed feelings, despite his rink finishing the round-robin section of the competition with three defeats.
"In some ways it is bitter-sweet because we've wanted to get over the finish line for a while and we've just not managed it," he said.
"The Chinese guy (Liu Rui) was on fire there. It's tough when you are up against a skip who is making everything.
"We knew we had a lot of tough games at the end. We knew we needed to win one of them but unfortunately we didn't, but we have just got to take what we have got.
"We're not out, so we're not going to be too downbeat about things. We are still in this and a certain curler from GB won coming from this spot before, so we will see what happens.
"We have a good record against these guys (Norway). Obviously we didn't win this week against them, but we actually quite enjoy playing against them.
"We're used to their style of game, we know what we're going to get and what to exploit.
"They know our game very well but, if we play like that, I am pretty confident we will win the game."
The "certain curler" Murdoch was referring to was Team GB's current women's curling coach, Rhona Howie.
Under her former name, Rhona Martin, she skipped the British team to their most recent gold medal in the sport, at the Salt Lake City Winter Olympics in 2002.
However, her rink had to win two tie-break matches just to reach the semi-finals.
Murdoch believes his task will be no less difficult due to the rising standard of opposition in modern-day curling, exemplified by China.
"To be honest it was only a matter of time before they emerged, we knew they would come good eventually," he said.
"The standard of this Olympic Games is the highest I've ever seen.
"Look at the teams out there, look at Denmark beating Norway, the standard is incredibly high, that's the way it is. Curling is a tough sport."
Norway's Haavard Vad Petersson knows there will be few secrets between the two rinks when they line up against each other on Tuesday.
He said: "We've had about 200 battles against Murdoch. We beat them in the round-robin but we lost to them in Europeans a couple of months ago, so it's going to be a close one. Both teams have a good chance. "
Team mate Christoffer Svae was "just happy we've got another chance", but remains confident of making it through to the last four.
"We will have to play better than we have done so far," he said. "But in the last couple of years, we have won more than we've lost against them.
"They have a tendency to play much better at championships. It seems like they care more. But we won the last time (in round robin), so I think it will be pretty close."