Kenin got a point back, but Andreescu's backhand victor sealed the match and brought the Canadian to her knees.
Andreescu said the emotional display was automatic after a gruelling second set that had her face five match points.
The Canadian missed a clear opportunity to go up 6-3 in the second-set tiebreak when she sailed an overhead smash long.
Playing to her hometown crowd, Andreescu put her hand to her ear like Hulk Hogan to egg on the cheers after the victory. "I think it pumps me up even more. All I can say is I'm just so happy to be back on court right now", Andreescu said.
"Just with all that I've been through. Life is freaking incredible right now".
Andreescu shot to prominence with a victory at Indian Wells in March, but this week marks her first tournament since she was forced out of the French Open with a shoulder injury.
She was taped up again for the semifinal against Kenin, the last woman to beat Andreescu in a full match at the Mexico Open in Acapulco back in February.More news: Hong Kong residents demand release of arrested woman
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When healthy, Andreescu has been virtually unstoppable this season.
Andreescu, who has dealt with several injury setbacks in her young career, looked to be in trouble when she gingerly returned to the court from a medical timeout late in the second set with her right thigh heavily taped and her movement hampered.
Asked if she would consider herself a perfectionist on and off the court, Andreescu replied: "Yes, definitely".
Pliskova's chances of replacing Australian Ash Barty, who lost here in the second round, atop the world rankings are over and Japan's Naomi Osaka, who plays later on Thursday, will move back into first spot.
The opening set was everything and more one would expect from a Premier level Saturday showdown. "I'm just going to try and stay in the present moment". On her three-set win over Karolina Pliskova, Andreescu added: "I've been practising a lot on trying to figure out what to do in this kind of circumstances".
Earlier, both players showed impeccable defence, leading to long rallies, none better than the one capped when Andreescu ripped a victor off the net cord to rouse the crowd.