Andreescu, who shot to prominence with her Indian Wells triumph in March, extended her dream run in her home country when she fired a backhand winner on her fifth match point.
For Andreescu, who made her return to action in Toronto after missing the last few months with a shoulder injury, the win was her first two-set victory all week after having spent more time on court than any other player.
"I've been through so much the past two months, and all I can say is I'm so happy to be back on court," an emotional Andreescu said on-court.
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"I'm glad it was two sets today, but it wasn't easy. I was so so nervous and I just felt like crying after because I'm just so happy. I'd say this is even bigger than winning Indian Wells."
A relieved Andreescu, in her first tournament since she withdrew from the French Open ahead of the second round, dropped to her knees and kissed the blue hardcourt while the home crowd screamed her name.
Andreescu had to fight plenty of nerves as she struggled to put away Kenin, who won three consecutive games in the second set to level at 5-5.
When Kenin lost the next game she took a medical timeout and left the court to get treatment on what she later said was a groin injury.
Kenin returned to the court and won a lengthy seven-deuce game to set up the tiebreak during which there was little to separate the players until Andreescu ripped the backhand winner to end the match.
The unseeded Canadian has knocked out some big names this week, including Dutch fifth seed Kiki Bertens in the last 16 and Czech third seed Karolina Pliskova in the quarters.
Andreescu, who improved to 3-1 in career meetings with Kenin, will face three-times champion Serena Williams or Czech qualifier Marie Bouzkova in Sunday's final.
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