Azarenka, beaten in the US Open final less than a week ago, has transitioned to the clay courts in impressive fashion after beating Venus Williams and now, more impressively, Kenin.
The Australian Open champion had no answer to Azarenka's ruthlessness and near-perfection out on court in Rome, with the Belarusian claiming victory in just an hour and one minute.
Azarenka faced no break points in the entire match and made only one unforced error as she emphatically took the first set against a player who was her US Open doubles partner.
Kenin improved in the second set, forcing some long games – particularly the second, which was at deuce on five different occasions.
But Azarenka – who faces Russian Daria Kasatkina in the last 16 – simply had too much for the American and cruised to a sensational victory over the third seed,
"I think my consistency was the key to the scoreline," Azarenka said. "I feel like I played really smart tennis today: I was able to use a lot of court; I was able to use a lot of different pace.
"So, I'm very happy with that. But the key was definitely being able to maintain the level that I started with."
Earlier, Garbine Muguruza managed to outlast American sensation Coco Gauff 7-6 (7-3) 3-6 6-3 in an absorbing contest.
Gauff, 16, appeared to be in control of the decider after an early break of serve.
But three double faults in the following game gifted Spaniard Muguruza an instant break in return, giving her the initiative to go on and seal victory.
Johanna Konta saw off Irina-Camelia Begu in fine fashion, the seventh-seeded Briton emerging 6-0 6-4, but Kiki Bertens and Petra Martic were not so impressive.
Bertens, seeded fifth, fell 6-4 6-4 to Polona Hercog, while eighth seed Martic succumbed to Yulia Putintseva in a gruelling three-hour contest, the latter eventually winning 6-3 6-7 (2-7) 6-4.
Marketa Vondrousova and Svetlana Kuznetsova were among the other victors on the day.