Jones' Winnipeg squad dropped a 7-6 decision to Switzerland's Alina Patz in the late draw Wednesday to snap its five-game win streak. It came after the Canadians captured a 9-3 victory over Norway.
Jones will head into the final day of round-robin play Thursday needing one more win to clinch playoff berth.
Switzerland (8-1) moved atop the overall standings and assured itself of no worse than a tiebreaker scenario. Canada (7-2) will play twice Thursday, facing Germany's Daniela Driendl (4-5) and Japan's Ayumi Ogasawara (5-4).
"I think we just didn't have the start we wanted and we kind of had to battle back," said second Jill Officer. "We certainly had some opportunities in the last couple ends, but it just didn't work out for us.
"We'll have to win out (Thursday) and hopefully that does good things for us."
Two wins Thursday would secure Canada a berth Friday in the Page playoff 1-2 game.
"It's all you ever want, to have destiny in your own hands," said Jones. "We know that we have to come out and win both (Thursday) and we'll find ourselves in a really good spot.
"It was a big loss tonight, but that usually makes us play a little bit better."
Patz made to clutch shots in the first end to thwart a Canadian steal and register two points before adding a steal of her own an end later.
Canada countered with two in the third and fifth ends with a single by Switzerland sandwiched between. The Swiss took the lead for good with two in the seventh after Jones barely missed consecutive chances to get out of the end with a double takeout.
"She (Patz) played great and you can't take that away from her, and we missed a couple of key opportunities to maybe take some extra points," said Jones. "Hopefully we'll have another chance to play them.
"It's a tough loss to take this late in the week, but we have another opportunity (Thursday) to win two and have ourselves in a really good position for the playoffs."
Patz said the win over Canada was important for the Swiss squad.
"We played really well and we had to play really well to beat them, it's always a pleasure to beat the Olympic champions," she said. "I felt really comfortable, we started really well and that made us self-confident and I think that was a key point for us."
The top four teams following the completion of round-robin play will advance to the Page playoffs.