Second seed Karolina Pliskova suffered a scare in her opening match at the Madrid Open, before overcoming Lesia Tsurenko in three sets.
Pliskova, the world number three, was forced to come through a tie-break in the first set and was then well-beaten in the second.
However, she came through the decider to triumph 7-6 (7-5) 2-6 6-2 and book a second-round meeting with Anastasija Sevastova, a 6-2 6-4 winner over Zhang Shuai.
Sixth seed Johanna Konta was the biggest casualty of the day, losing in three sets to Laura Siegemund, ninth seed Madison Keys also bowed out, while Eugenie Bouchard could face Maria Sharapova in round two after overcoming Alize Cornet.
Bouchard was highly critical of Sharapova last week as the former world number one made her return from a 15-month ban in Stuttgart.
PLISKOVA TAKES POSITIVES FROM TSURENKO BATTLE
Pliskova feels she could benefit from having been pushed in her opening match.
The Czech said in a news conference: "Maybe it's better that I won it in this way, not in the way where I wanted to win, like 6-2, 6-2.
"Maybe it's better that I got little bit through this difficult situation, not really feeling well on the court, not having my serve always there.
It's an important win. Every first round, it's tough, [it] doesn't matter which surface. So far, I'm struggling a little bit on the clay."
KONTA LOSES MARATHON
Up a set and 3-0 in the final set, everything looked good for Konta.
But Konta was outlasted by German Siegemund, who triumphed 3-6 7-5 6-4 in a stunning late night encounter.
The match finished at 02:17 local time in the Spanish capital.
LANDMARK WIN FOR DOI
Prior to Saturday, Japan's Doi had played 13 matches against top-10 opponents ... and lost the lot.
Doi also arrived in Madrid having lost her last five WTA Tour contests, so it was something of a surprise to see the world number 52 dump out Keys.
The American won more points, but was made to pay for a host of unforced errors as Doi triumphed 6-4 4-6 6-4.
VINCI WINS SEESAW AFFAIR
It is fair to say the match between Roberta Vinci and Daria Kasatkina featured two significant shifts in momentum.
Vinci triumphed in three sets to book a potential second-round clash with third seed Simona Halep, who faces Kristyna Pliskova in her opening match.
However, the score was an unusual one as Vinci won 6-1 1-6 6-1.
The other round-one winners were Alison Riske, Kiki Bertens, Anastasija Sevastova, Irina-Camelia Begu and Lara Arruabarrena.
HAPPY BIRTHDAY, DOMINIKA!
Dominika Cibulkova was not in action on Saturday, but did speak to the media.
And her news conference was briefly interrupted by the arrival of a birthday cake, in celebration of the Slovakian turning 28.