Ruse had her chances on Friday, not only winning the first set, but going up an early break at 3-1 in the third set. She forced Rybakina to serve to stay in the match at 4-5 in the decider, too.
But the Kazakh hung on every time she was in trouble, eventually holding for 5-all, breaking for 6-5 and serving it out.
"Today I basically survived," she said afterwards. "It wasn't my greatest performance, but she was playing very well, very deep and aggressive, so it was very difficult. Also my serve was not really helping me today. But I'm happy I managed to win and hopefully I can bring better tennis in the next round."
Awaiting the No. 2-seeded Rybakina in the third round will be No. 32-seeded Zheng Qinwen, who also had to battle back from a set down to win her opening match in Madrid on Friday, defeating American Sofia Kenin, 1-6, 6-3, 6-3.
Rybakina leads Zheng in their head-to-head series, 3-1, but this will be the pair's first career meeting on clay courts.
