Cirstea has put together the best run of her career, taking out two former number one ranked players in Caroline Wozniacki and Jelena Jankovic, and then two former grand slam champions in Petra Kvitova and Li.
The 23-year-old Cirstea was by no means perfect in Saturday's semi-final, but was resourceful and did not implode when the pressure was on.
"I think that's a big change for me," she said.
"Before, I would get down on myself, while now I just try and focus every single point and I don't care so much what's just happened in the past."
Cirstea raced through the opening set in just 21 minutes as Li, last year's Rogers Cup finalist, was wild and inconsistent.
But the former French Open champion picked up her game in the second set, breaking Cirstea to lead 3-1 when the Romanian dumped a backhand into the net.
Li fought off three break points in the next game and appeared to have control of the set when Cirstea sought advice from her coach Darren Cahill.
Cirstea broke Li when she was trying to serve out the set at 5-4 then broke her again to snatch a 6-5 lead.
Although she failed to serve out the match herself, squandering two match points, then fell 4-1 behind in the tiebreaker, she regained her composure as Li started to falter, handing victory to Cirstea on a double-fault.
"She's got a lot of confidence now," Li said. "Sometimes I was feeling she couldn't hit a winner, but the ball came to you as a winner. It's very tough."
Cirstea's opponent in Sunday's final will be either Serena Williams or Poland's Agnieszka Radwanska, who were due to meet in the second semi-final on Saturday night.
"If I want to win this, I have to step it up," said Cirstea. "I had to win it on my terms."
(The story fixes dateline to August 10)
(Reporting by Matt Cronin; Editing by Julian Linden)
