After Kyle Smith's men's rink secured a comprehensive 10-3 win over Norway, Eve Muirhead's women's squad edged to a 8-6 win over Japan. Both now have five wins from eight games.
Wins on Wednesday for the men against the United States and the women against Canada will see Britain progress to the semi-finals and avoid any play-offs.
"We knew we had to win that one," women's vice-skip Anna Sloan said.
"We're in a good position, maybe not the best, but we're going in the right direction."
Japan had won five of their prior seven games and stole three points on the second end to take the initiative.
But Muirhead, Sloan, Lauren Gray and Vicki Adams - bronze medal winners four years ago in Sochi - retained their composure, stuck to their game plan and came out on top.
Sloan added: "We enjoyed it and I thought we played really well. We controlled the game and that's important at this stage.
"I think we're all pretty relaxed out there and we play well like that."
It has been a topsy-turvy tournament so far for Muirhead's rink, but after successive losses to hosts South Korea and Sweden, the Britons are back on track.
"We were at the wrong end of the inch in a couple of games that could've easily gone our way," Sloan added.
"And it left us in a 'we have to win' situation. It's been really tough, but our experience has been shining through."
Coach Glenn Howard said: "It was a huge win. We didn't talk about it but to me that was a massive game. It was a not a must-win but an incredible game to win.
"To go to 5-3 and put ourselves in a great position...we know that if we win tomorrow that puts us into the final four, which is your first goal.
"The beauty is we're getting a little bit better. We're making a lot of key shots and that's the sign of a championship team.
"We now control our own destiny. We know that we win, we are in."
This is the third Olympics for Muirhead's rink, but it is the first for Kyle Smith's.
When Kyle Smith, his brother Cammy Smith, Thomas Muirhead and Kyle Waddell were selected last June - ahead of David Murdoch's silver-medal winning squad from Sochi 2014 - eyebrows were raised.
But they answered their doubters emphatically on Tuesday by stunning 2014 world champions Norway into submission.
Thomas Ulsrud's Norway squad, renowned for their colourful trousers and silver medallists at the Vancouver 2010 Games, struggled as the quietly spoken Kyle Smith put in a more flamboyant performance.
And the Norwegians conceded defeat after seven ends.
After five wins from eight games - and three in a row - Kyle Smith was overjoyed.
"It's just pleasing we've managed to put a good string of wins together now and we're in a position where we're in control of our own destiny," he said.
"It gives everyone else a bit of confidence in us as well, I hope. We've always believed in our own ability.
"We've had a couple of games where we haven't played our best but we've still managed to come through and win. If you're doing that you're doing something right. It does a lot for confidence."
Ulsrud's accuracy deserted him, but Kyle Smith was metronomic.
"I had a good feeling this morning," he added.
"For us to come out and play like that against them shows just what we're made of."
Britain men's coach Viktor Kjell was delighted with Smith's form, saying: "This was his best game. It's good for the team's confidence as well, to get a big win like this against a tough opponent."
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