Two players who hope to leave New York with the world no. 1 ranking took positive steps in that direction on Thursday as Karolina Pliskova and Elina Svitolina advanced to the third round of the US Open.

Pliskova had to overcome a strong effort by American Nicole Gibbs to survive, 2-6, 6-3, 6-4. Gibbs quickly took charge in the first set using her quickness and defense to move Pliskova around the court. The Czech was out-of-sorts as she struck 15 unforced errors and her big weapon – her serve – let her down. She was only able to place 56 percent of her first serves into play and misfired with 4 double faults and Gibbs found success against her second serve as Pliskova won just 29 percent of those points.

Each player attempted to impose their style in the second set, but Pliskova began to serve successfully and reduced her unforced errors. And with Gibbs serving at 3-4, the current world no. 1 found a service break. She would consolidate and take the set.

Both players continued to battle in the third but Pliskova elevated her game, fueled by her big serve. She won all 17 of her successful first serves in the set. Nevertheless, Gibbs had a look at a break opportunity to take a 3-1 advantage, but Pliskova held which appeared to tilt the momentum in her favor. Then, with Gibbs serving at 3-4, the Czech broke through gaining the one service break she would need to take the set and the match.

Pliskova acknowledged the value of her serve afterward, “In some matches, you need the serve more than normal,” she said. “That was the case today. I didn’t feel that my game from the baseline was that good today, so I’m just happy that I had my serve.”

She will advance to play Shuai Zhang in the third round.

Meanwhile, 4th-seeded Elina Svitolina advanced past Evgeniya Rodina 6-4, 6-4.

Svitolina was never really tested in the match and had things on her terms for most of it. Her played dipped late in the second set but she rebounded to close it out in straight sets.

Svitolina is back to familiar territory in New York. She advanced to the third round in each of the last two years and hopes to break through in the second week of play.  She will face Shelby Rogers next.