The Czech player, who returned to action in May after an attacker at her home in December stabbed her in the hand, lost the first set heavily to Estonia's Anett Kontaveit.

However, she was able to recover and came through 1-6, 7-6, 6-3 at the Lindner Family Tennis Center in Ohio.

There was also success today for 2015 US Open finalist Roberta Vinci, with the Italian ousting Tímea Babos of Hungary 7-5, 7-5 on the hard courts.

However, Puerto Rico's Olympic champion Monica Puig was knocked out, going down 3-6, 6-3, 6-2 to American Taylor Townsend.

The draw had thrown up an interesting clash between Russia's five-time grand slam champion Maria Sharapova and this year's French Open winner Jeļena Ostapenko of Latvia.

However, an arm injury suffered by Sharapova - who returned from a 15-month drugs suspension in April - meant she did not take to the court.

Ostapenko will instead meet a qualifier tomorrow. 

In the men's competition, home players John Isner and Sam Querrey were among those to make it through.

Querrey, the semi-finalist at Wimbledon this year after he beat Britain's world number one Andy Murray, proved too strong for compatriot Stefan Kozlov, romping to a 6-3, 6-0 victory.

Isner knocked out Serbia's Viktor Troicki with a 7-6, 6-4 success.

Croatia's big server Ivo Karlović needed three sets to oust Jiří Veselý of the Czech Republic, 6-3, 3-6, 7-5.

Spain's four-time Davis Cup winner Feliciano López came through against Chung Hyeon of South Korea, 7-6, 6-1.

The tournament, an Association of Tennis Professionals World Tour Masters 1000 event for men and a Women's Tennis Association Premier 5 competition for women, continues tomorrow.

All of the top seeds will enter in the second round, with Spain's Rafael Nadal due to overtake the injured Murray as world number one. 

It is a key build-up event for the last grand slam of the season, the US Open, which begins in New York City on August 28.