The No.7-seeded Errani never lost serve - in fact she only faced one break point in a total of eight service games - and broke serve four times en route to a 63 61 victory over Urszula Radwanska.
"I won the first set with just one break, but many of the games went to advantage so it was maybe harder than the score looks," Errani said. "I don't think I played an incredible match, but for the first match of the tournament it was enough, and I'm very happy to be in the second round now."
Errani was also asked about the court and the conditions. "The courts this year are perfect," she said. "Of course, Madrid is at an altitude so it's a bit fast, but the courts are really perfect this year."
And what has the Italian been up to since her busy Fed Cup and Stuttgart week? "After Stuttgart I went back to Valencia and practiced there before coming to Madrid three days ago," she said. "I've been living in Spain for nine years so I'm comfortable here and am always very happy to play here."
Errani now has a WTA-leading 26 match wins on the season, breaking a tie with Serena Williams.
The only other Top 20 player in action was Sloane Stephens. Stephens, who at No.17 was a spot out of the seedings this week, was ousted by Daniela Hantuchova, 63 75. Hantuchova, a wildcard here, got her third Top 20 win of the year, having beaten Errani and Maria Kirilenko earlier in the season.
Other winners were Kirsten Flipkens, Julia Goerges, Alizé Cornet, Sabine Lisicki, Laura Robson and Lourdes Domínguez Lino, who wrapped up the night session with a 62 46 64 grinder over Simona Halep. Robson was also pushed to three but eventually beat Magdalena Rybarikova, 67(4) 62 62.
"I've had a tough couple of matches in my last few tournaments so it's good to finally win one," Robson said afterwards. "I'm looking forward to doubles tomorrow with Lisa Raymond - I'm really excited to play with her again - and today was just a great match for me. I'm really happy with the win today."
"I woke up this morning and my stomach wasn't feeling very well, but I served too well today," Goerges said. "That was the key, because I couldn't really run left to right. But I couldn't show any negative emotions, I just had to stay positive, and it's good to get a win like this. I'm very happy about it."
"I had some troubles physically in the middle of the second set but I just kept fighting, and I'm happy I got through because Kiki's a really good player," Cornet said after her match. "I hope it's going to keep going like this for me, because I have a lot of expectations on clay. It's my favorite surface."