Playing her first ever match at the Premier-level tournament, Suárez Navarro looked sharp against Japanese qualifier Sachie Ishizu, storming out of the blocks to a 4-0 lead and never really looking back after that, eventually moving on in straight sets in just 69 minutes over on Stadium 2, 64 63.
She was beaten to the finish line by the Stadium court match, though, as American qualifier Coco Vandeweghe threw down 12 aces to take out American wildcard Allie Kiick in just 62 minutes, 61 62.
"Everything was clicking today, on the returns and on the serves, and even in the rallies, so I'm happy with my performance and couldn't ask for anything better," Vandeweghe said. "I love coming and playing here in the American hardcourt series and I love playing at home. I'm really ready to go."
Did winning three qualifying matches help or hurt Vandeweghe? "I felt really good going into today's match - I had already played three matches so I was used to the courts and everything like that. It definitely helped that I had gone through qualifying so I had the experience on these courts here."
"Cibulkova's on top of her game right now, in terms of on a high, I mean you win Stanford and you're definitely going into the next week feeling good about yourself," Vandeweghe said. "Ana is always a tough opponent, former Grand Slam champion - you can't take either one of those opponents lightly."
The other three daytime matches saw Urszula Radwanska come back from a break down four times in the first set en route to a 76(3) 64 win over Kiwi qualifier Marina Erakovic, Kazakh qualifier Sesil Karatantcheva rally from 3-1 down in the first set and 5-3 down in the second set to close out Julia Goerges, 63 75, and Laura Robson come back from the brink of defeat against Ayumi Morita, who served for the match at 64 54 and was two points away at 30-0 but fell to the British No.1, 46 75 62.
"It was really tough today - Ayumi was playing super, super well," Robson said. "It felt like every time I hit a good shot, she would hit a better shot. So I just had to stick with it and wait for my chance.
"After I broke her back at the end of the second set, I felt the momentum on my side again."
"It was definitely unexpected because Tamira's a great player," Hantuchova said. "I didn't make too many mistakes, everything worked, I actually surprised myself. I'm glad to be in the second round."