Carla Suarez Navarro and Karolina Pliskova kept their slim hopes of reaching the WTA Finals alive with victories at the Kremlin Cup.
The players headed to Moscow 11th and 12th respectively in the Road to Singapore, but could yet climb into the top eight should things go their way this week.
Suarez Navarro needs to reach the final to have any chance of making the season-ending showpiece and kicked off her campaign with a 6-4 7-5 second-round win against Dominika Cibulkova.
Having initially fallen a break behind, Suarez Navarro recovered to edge the first set, before converting her third match point to wrap up a scrappy second.
For Pliskova, only victory here will give her a chance of competing at the Finals and she triumphed 6-4 5-7 7-6 (9-7) over Alexandra Dulgheru in the first round.
Pliskova looked on course for a comfortable victory when she moved 2-0 ahead in the second set, but was forced to a decider - eventually prevailing after falling 4-1 behind and saving a match point at 6-5.
Eighth seed Anna Karolina Schmiedlova triumphed 6-4 6-3 over qualifier Aliaksandra Sasnovich, while Kristina Mladenovic opened with a 7-6 (7-4) 6-3 win against Ana Bogdan.
Elsewhere, there were wins for Anastasija Sevastova, Anastasia Pavlyuchenkova, Daria Gavrilova and Daria Kasatkina against Olga Govortsova, Monica Niculescu, Alize Cornet and Paula Kania respectively.