Elise Christie and Jack Whelbourne came through five heats each at the opening short-track Olympic qualifier in Italy to leave GB on the cusp of earning their first places at the Sochi Games.
While not mathematically certain, their results in Turin should earn berths in the men's and women's 500m and 1500m.
"Right now we're both in a good place, we're both skating well," 22-year-old Whelbourne told BBC Sport.
Olympic qualifying for short-track skating concludes in Russia next week.
But the points-based qualification system means British skaters have broadly targeted a last-16 finish in their Turin events, which is expected to get them to Sochi 2014 regardless of next week's performances in Kolomna.
Once confirmed, places will be awarded to Great Britain as a nation rather than individual skaters - who must wait for the British Olympic Association to ratify their selection and confirm their names later this year.
"It's looking good," said Whelbourne. "Hopefully we can build on that and move forward. If we put a performance similar to this out next week, we'll be looking good for Sochi."
Christie struggled at the season's two opening World Cups, battling mumps before suffering the loss of her grandmother while away racing in Asia, both of which affected her form.
However, she won all five of her heats on Thursday to book places in the quarter-finals of both the 500m and 1500m, with her favoured 1000m distance still to come.
"After how hard the past few months have been, it's nice to feel some relief eventually," said the 23-year-old.
"My skating has been strong. The ice isn't great so everyone has been skating a bit slow, but it's been good, everything has gone well."
While merely the third World Cup of the season on paper, this week's dual status as an Olympic qualifier means it is perceived by many athletes as being harder than racing at the Games itself.
Entry lists are packed with skaters trying to earn enough points to reach Sochi 2014, leading to 13-hour days of racing as the field is whittled down to the lucky 32 (or 36 for the 1500m distance) who will go to the Olympics.
Britain's Charlotte Gilmartin was an early casualty on Thursday as she crashed out in her opening 1500m heat, clipping skates with a rival before clattering into the padded hoardings surrounding the ice.
Gilmartin later failed to make it through the 500m heats, joining Alex Stanley and 16-year-old Kathryn Thomson, neither of whom progressed from Thursday's preliminary races.
In the men's events, Jon Eley - a veteran of the 2006 and 2010 Winter Olympics - was controversially penalised in the heats of his preferred 500m.
American skater Eduardo Gonzalez leapt in front of Eley while rounding a corner, causing Eley to collide with Gonzalez, an offence for which Eley was disqualified.
But Paul Stanley went through to the 500m quarter-finals as the third-fastest in his heat.
Earlier, Richard Shoebridge failed to come through his 1500m preliminary round. The 28-year-old had been handed a tough draw featuring former European champion Thibaut Fauconnet of France, South Korean six-time world champion Noh Jin-kyu and rising US star John-Henry Krueger.
No Briton has won a medal in short-track skating at the Olympics since the Lillehammer Games in 1994, where Nicky Gooch - now a member of the GB coaching staff - took 500m bronze.
Christie is seen as the team's leading medal hope for Sochi. She has been the women's world number one over 1000m for much of the past two years, winning world bronze in the event earlier in 2013.