The Olympic champion earned a 9-4 win over Scotland before dropping an 8-6 decision to Sweden. That left Jones with a 2-1 record, standing fourth in the overall standings behind unbeaten China, Russia and Switzerland (all 3-0).
"To be honest, we had a really tough day so to split the day we have to be happy with that," said Jones. "We just didn't play as well as we would've liked (against Sweden), which was unfortunate."
Jones couldn't have started better against Sweden, taking three in the first end. But the Swedes countered with two in the second before stealing one in the third.
Sweden then scored three in the eighth for a 7-5 advantage.
"After the first end, we played a really good game," said Swedish skip Margaretha Sigfridsson. "There were some tough ends but we managed to keep our rocks in good places and we played really well during the game.
"We'll take confidence from this."
Jones beat Sigfridsson to win gold at the Sochi Winter Games last year.
"I thought we controlled the first part of the game," Jones said. "But we had a chance to get another big end in the third and we kind of botched that a little bit and ended up giving up a steal. I think that turned the game around a little bit."
Canadian second Jill Officer fell twice while sweeping in the fifth end, the first time landing heavily on her right leg.
"Right now, I don't feel anything," she said. "I suspect (Monday) it could be a different story."
Against Scotland, Jones led 5-2 by the fifth end and sealed the lopsided affair with two more in the seventh and another two in the eighth and final end. The Scots, skipped by 2013 world champion Eve Muirhead, managed just one in the third, another in the fourth and two in the sixth.
"We made really precision draws in the first end and that started us off well and gave us some confidence," Jones said.
Jones beat Finland 9-6 in her opening game Saturday. Canada returns to the ice Monday to face China and Russia.
"We knew we would have to be strong from start to finish (Sunday), and I think we just let it slip away," said Officer. "We just have to regroup.
"We had a really good game against Scotland earlier and there were a lot of positives we could take away from this game as well."
Jones' team is trying to become the first reigning Olympic champion to win both the Canadian and world championships the following season.
The top four teams at the end of round-robin play will advance to the Page playoffs.
A Canadian team hasn't won gold at the women's world event since Jones did so in '08 title. Jones, a five-time national champion, made her world championship debut in 2005 and won a silver medal in 2010.
Canada leads all countries with 15 gold medals and 31 podium appearances at the world championship since 1979. Sweden is next with eight gold and 23 total medals.