"CoCo is always going to be a tough person to have to try to get returns in," Keys said during her on-court interview.
"She obviously raised her level in the second set, so then I had to as well in the third.
"From then it was just about who could get more balls in at the end."
Keys, who has never advanced beyond the second round in Cincinnati, will next face unseeded Russian Daria Kasatkina.
In earlier action, Australian Daria Gavrilova shook off an uncertain second set to defeat France's Kristina Mladenovic 6-0 7-6(6).
After cruising through a perfect first set, the 23-year-old Gavrilova needed to save a set point in the second to hand the 13th-seeded Mladenovic her third straight loss.
"She has a history of great comebacks. She has done it at the French Open almost every match," said Gavrilova.
"She stepped up her game and was playing a bit looser and was not making as many unforced errors because the first set was not a great set from her."
Gavrilova moves on to face Italian Camila Giorgi in the round of 32 on Tuesday.
Big-serving Czech Petra Kvitova battled back to defeat Anett Kontaveit 1-6 7-6(2) 6-3 in Monday's opening match.
Kvitova, the tournament's 14th seed and a two-time Wimbledon champion, will face either wildcard American Sloane Stephens or Czech Lucie Safarova, who play on Tuesday.
(Reporting by Rory Carroll and Frank Pingue; Editing by Janet Lawrence)
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