Britain's women curlers booked their place in the Sochi 2014 semi-finals on Monday but the men were left facing a play-off showdown with Norway on Tuesday for a last-four spot of their own.
Eve Muirhead's world champion rink of Scots beat Russia 9-6 in their morning match before a combination of other results meant they were through to the semi-finals, irrespective of their result in the later encounter with Denmark, which they lost 8-7.
Britain held a 3-2 lead against the Danes 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 Britain allowed the Danes, in possession of the hammer, to register three in the 10th, forcing an extra end.
Lene Nielsen's rink then stole a point from it to wrap up an 8-7 triumph when Muirhead misjudged her final stone delivery.
After finishing fourth in the round-robin rankings, Britain are due to face unbeaten Canada in the semi-finals on Wednesday at 1400 local time (1000GMT). Sweden and Switzerland meet in the other semi-final.
Earlier, Muirhead's rink took four to go 7-3 ahead of the Russians in a terrific eighth end. The host nation rallied with three shots in the ninth but Muirhead, with the hammer, executed a double take-out on her final shot to ensure victory.
Britain's men were left with a play-off battle against Norway at 0900 (0500GMT) on Tuesday after both teams suffered defeat in their final round-robin matches.
Murdoch's men were up against it after the Chinese stole a crucial point in the eighth end to move 5-3 ahead. Britian pulled two back in the ninth before their opponents settled it 6-5 in the 10th with the final stone.
By the time that match had finished, though, the Norwegians had already gone down 5-3 against the Danes, meaning Norway and Britain finished the 10-team round-robin stage in joint-fourth, each with records of five wins from nine fixtures.
Norway go into the play-off match with a 7-6 round-robin win over Britain under their belts, but Murdoch is not reading much into that.
"We have a good record against these guys (Norway)," he said. "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."
Sweden, Canada and China qualified for the semis in first to third positions.
Great Britain bobsleigh pilot Lamin Deen will turn his attention to the four-man competition later this week after finishing in 23rd place in the men's two-man event at the Sanki Sliding Center.
Deen shaved almost half a second off his previous run time as he came down his third run in 57.38 seconds, but it was not enough to make the cut for the fourth and final run, for which only the top 20 sleds qualify.
But both Deen and his brake-man John Baines believe their continued improvement over the two-man competition bodes well for when they join up with Ben Simons and another as yet unconfirmed team-mate in the GB2 sled for the four-man competition, which begins on Saturday.
Baines said: "Every time we have pushed together we have got faster and I think that shows great promise for the four-man. I think we will move up six to eight places. We're really confident and I think we're going to shock a few people."
Deen has made no secret of his preference for the four-man competition in which team-mate John Jackson and his GB1 sled will start as genuine medal contenders.
Deen said: "I prefer the four-man - it's a lot sturdier and it's like comparing a race car with a truck. I like the team spirit and how much more technical it gets - and it's a lot faster."
Ice dance duo Penny Coomes and Nick Buckland completed their programme at the Iceberg Skating Palace with a top-10 finish.
Coomes and Buckland, both 24, won a European Championships bronze in January and maintained their progress in Sochi.
They went into the free skate section of the competition with a score of 59.33 from their short programme on Sunday night, and their Russian coach Evgeny Platov was looking for a top-10 finish.
Their thrilling routine to a medley of Michael Jackson music engaged the crowd and the mark of 91.78 gave them a total of 151.11 to leave them in 10th place, with Coomes looking to peak in Pyeongchang when the next Winter Games come around.
"I really want to come back in four years' time and get that medal, that's what we're going to strive for every day," she said.
Buckland added: "I know we have skills to perfect, we have to mature and to take it to a new level. But I feel we are competitive now and that will carry us for the next four years."
Platov is eyeing a medal for the British pair in Pyeongchang in 2018.
He said: "I'm pleased but I'm never satisfied. They will improve, they have four years before the next Olympics.
"We have to add endurance, speed and improve on technique. The next target is four years and medals."