Sweeting, who will play Rachel Homan of Ottawa for the women's championship on Sunday, scored a single in the 11th end to secure the semifinal victory.
Nedohin gave up a steal of one in the ninth end and allowed Sweeting to escape without having to throw last rock in the 11th. Nedohin's last-rock raise attempt was wide and left Sweeting sitting with the winning point.
Both skips struggled at times, finishing with their lowest shooting percentages of the week, both at less than 70 per cent.
"Did they shorten the rings of something overnight?" Sweeting joked afterwards. "It was quick out there. I was heavy a lot, but I made the ones that matter, that's what counts."
She credited her teammates with playing a major role in the victory.
"The whole team hung in there. I was struggling a bit with my draws but the team was really good, they were just, 'You know what? We've got this, it's ours.' They really hung in there."
Though Sweeting struggled with draws, she made the key shots, including a perfect draw to the button for two in the eighth and her first lead of the game.
Nedohin counted one in the first, two in the third, one in the seventh and two in the 10th to force the extra end. Sweeting countered with one in the third, deuces in the fifth and eight and a steal of one in the ninth.
"I missed the shot," Nedohin said of her try at a come-around tap back in the ninth. "When your skip misses a shot in nine and they get a steal it's the turning point, absolutely. My thoughts were to get two, maybe an opportunity for three."
The game swung in Sweeting's favour in the eighth end when she made a tight but perfectly placed draw to the button for two and a 5-4 lead.