After dropping the first three games, Homan has now rebounded for two straight victories.
"I've never been so excited [to be 2-3]," Homan told CBC's Colleen Jones. "We've got an opportunity here and we wanna try and play our best for Canada."
Sunday's match was full of tense moments.
With the game tied at four in the sixth end, Homan missed a guard on her final shot — and the Swiss made her pay, nailing their final rock for a triple and a three-point lead.
From that point on, it was an uphill battle for the Canadians.
"I know we all wanted a couple of shots back there at times. but we stuck with each other and believed in making that next shot. It was a real character win — we had to grind it out and couldn't let off at all. Really proud of my team for how well they played," said Homan.
They scored two in the seventh to begin that climb, but Switzerland responded with a single of their own one end later.
The ninth end is when things began to turn for the Canadians.
Down two with the hammer, Canada's options were limited: a double would tie the match, but give Switzerland the hammer in the final end, and a single would likely end the game.
But Homan made sure neither happened. After Tirinzoni missed her final shot, mistakenly rolling a Swiss stone out of the house, Homan executed a clean knockout for a Canadian triple.
"I was just throwing it, so I was thinking about how that line ran and the weight we needed and I talked it over with the team to make sure that everyone's on the same page," said Homan.
Now, the Canadians had put the pressure on the Swiss in the final end after taking a 9-8 lead.
"I think we were just trying to go into a pretty good spot in the ninth end and hope that maybe we get a jam and hope for two, but if we put it in a really good spot and get a couple misses then maybe we can go for three," added team third Emma Miskew. "And that's exactly what happened."
Tirinzoni missed another shot in the 10th, as Homan stole a single and escaped with her second straight victory.
Struggles from 2nd
Still, Homan, Miskew, Joanne Courtney and Lisa Weagle have yet to play to the best of their abilities in Pyeongchang.
Homan curled at 83 per cent for the game — a slight improvement on her tournament average of 78 per cent. And Weagle and Miskew continued their solid play, remaining in the mid-80s.
But second Courtney repeatedly struggled against Switzerland.
She ended the game with a curling accuracy of 58 per cent, well below her tournament average. Her mistakes often put Canada in a tight position, but Miskew and Homan were able to wiggle out of some early end jams.
However, Courtney managed to find her footing when it mattered most, nailing some key shots in the final two ends.
"It's not how you start, it's how you finish, right? So I was just trying my best to stay in the moment and not get too down on myself and [I was] happy with the way I played the last two ends," said Courtney.
Canada now sits sixth in the standings, tied with the United States — both are one game under .500. But the Canadians control their own destiny for a potential semifinals berth after Great Britain fell to Sweden in extra ends.
The women will look to make it three in a row when they face off against Japan on Sunday night at 7:05 p.m. ET.