The British No.1 may have had an up-and-down start to the season, but she performed with gumption against her crafty and dangerous Slovakian opponent.
Konta coped admirably under pressure in the opener. She snatched an early break and overcame some tricky moments on serve before moving halfway towards her intended destination.
The British No.1 encountered turbulence in the second set, though, and slipped a break behind. Rybarikova was in the ascendancy, however Konta responded and then pushed for home.
At five apiece, the Slovakian dumped a sorry-looking backhand slice into the net to concede serve at a critical juncture. Konta clenched her fist as she moved 6-5 ahead, and she was contemplating her next challenge moments later.
It was a big win for Konta over a higher ranked opponent, and she will encounter Bernarda Pera, who defeated Aryna Sabalenka 6-4 2-6 6-3, next.
Defending champion, Simona Halep, tends to thrive in Madrid and Ekaterina Makarova was her latest victim. The world No.1 ruthlessly disposed of the Russian 6-1 6-0 in just 51 minutes.
“I think it was a great match,” the Romanian told the WTA website. “I played really well. Of course, maybe she [Makarova] didn't play her best, but she's always tough to play against. It was a good match and a good start.
“I was moving great. I felt the game and I like to play on this court. Always when I come back here, I feel a little bit more relaxed, so maybe that's why I can touch my best level every time I play. Hopefully, I can keep it also for the next round.”
Maria Sharapova arrived in the Spanish capital without a victory since January, but her losing streak is now over. The former world No.1 toppled Mihaela Buzarnescu 6-4 6-1 to finally get the winning feeling again.
“I want to be winning the right way,” said the reflective Russian. “I want to be making progress. I want to be present. I want to be competing, playing well and improving, but also I want to have a good outlook on things.
“I thought I did a really good job of improving a few things that weren't working well for me in the previous months. I guess that's all that I can expect from myself right now. Just keep putting that effort in on the court.”
Victoria Azarenka, in her first clay-court outing in nearly two years, shimmied past Aleksandra Krunic 6-3 6-3 to start her campaign on the right note. The former finalist will tackle Karolina Pliskova in a blockbuster second round clash on Monday evening.
Caroline Wozniacki, Garbine Muguruza, Petra Kvitova and Sloane Stephens all advanced in straight sets on a day of few surprises. Indian Wells winner, Naomi Osaka, is out, though, after a loss Shuai Zhang.