The 2011 champion in Charleston, Wozniacki cruised past Laura Siegemund 6-2 6-2 on the clay in South Carolina.
Wozniacki was one of 10 seeds progressing, with Mihaela Buzarnescu awaiting the Dane after the Romanian brushed past Lauren Davis 6-3 6-2.
Keys, the eighth seed and 2015 runner-up, was pushed by Tatjana Maria before getting through 7-6 (7-5) 4-6 6-4.
Jelena Ostapenko, Aryna Sabalenka, Belinda Bencic and Danielle Collins were also among the winners.
However, there were four seeded losers as Sofia Kenin, Elise Mertens, Julia Goerges and Anastasija Sevastova exited.
Monica Puig overcame Kenin 6-4 6-4 and Kaia Kanepi rallied past Mertens 0-6 6-0 7-5, while Goerges and Sevastova were beaten by Taylor Townsend and Jessica Pegula respectively.
At the Monterrey Open, four-time champion Anastasia Pavlyuchenkova impressively moved into the quarter-finals in Mexico.
Pavlyuchenkova, winner of the hard-court tournament in 2010, 2011, 2013 and 2017, cruised past Ivana Jorovic 6-0 6-0 in just 51 minutes.
Kirsten Flipkens, the 2016 runner-up, outclassed Dalila Jakupovic 6-3 6-3, Magdalena Rybarikova overcame Stefanie Voegele 5-7 6-2 6-3 and Sachia Vickery edged Nao Hibino 7-5 5-7 7-6 (7-5).