Fifth seed Angelique Kerber booked her spot in the second round of the Bank of the West Classic in Stanford after easing past Daria Gavrilova 6-1, 6-3 on Tuesday.
Kerber never looked to be in trouble throughout the match as she broke Gavrilova's serve three times in the first set en route to clinching it 6-1.
She then proceeded to break her opponent's serve twice more in the second set to finish Gavrilova off in an hour and five minutes.
All is all, Kerber proved to be too much for Gavrilova to handle as the German won 74 percent of her points on her first serve and also saved three of the four break points she faced.
Eighth seed Elina Svitolina had a much tougher time of it, eventually progressing from a closely-contested battle with Ukraine compatriot and qualifier Kateryna Bondarenko.
Svitolina appeared set for an early exit after losing the first set, but the 20-year-old rallied back to win the next two sets and finish off her opponent 4-6, 6-4, 7-5 in just over two-and-a-half hours.
The main upset of the day was provided by Japanese qualifier Kimiko Date-Krumm who recorded a superb 1-6, 7-6 (4), 6-2 come-from-behind win over world number 24 Sabine Lisicki.
Other players that will be joining Kerber and Svitolina in the second round are Ana Konjuh, Ajla Tomljanovic and Varvara Lepchenko.