"It was a good match," she said after the win. "She has a difficult game style, so she's tough to play against. But I was happy to start playing better to get the win."
Stephens has been one of the most impressive players of the season - capturing three titles in Auckland, Acapulco, and Charleston - but had stumbled in the opening hurdles of the Australian Open, BNP Paribas Open, and Miami Open. That dubious pattern was in danger of repeating for the 2013 Australian Open semifinalist, who dropped six straight games to lose the opening set from a double break advantage.
Undaunted, the American raced ahead by another double break in the second, and though Pereira clawed one back, Stephens duly served out the see-sawing second set, eventually engineering the win in just over two hours.
"I was just trying to make more balls than she was and just run around a lot," she said with a laugh. "I needed to be really patient."
Ranked just outside the Top 20, Stephens has gone on to win the title at every tournament in which she has won a match, but should face equally stiff opposition in the second round, as she next plays the winner of qualifier Patricia Maria Tig and Daria Kasatkina. The young Russian played Stephens in the quarterfinals of the Volvo Car Open, where she held a match point before falling in three sets.
"I still really haven't fully adjusted to the time difference, so I'm ok. It's like a 3 o'clock match for me right now!"
Earlier in the evening, French star Alizé Cornet outlasted a stirring challenge from Spain's own Paula Badosa Gibert, who won the opening set before succumbing to a bilateral leg cramp early in the third, 2-6, 6-2, 2-2, ret. Born in Manhattan, Badosa Gibert moved back to Spain at the age of seven and won last year's junior French Open title. For Cornet, the victory marks her first win on red clay this season, an important start towards defending the fourth round points she earned at Roland Garros nearly 12 months ago.
Of the other two seeds in action on Saturday, No.12 seed Elina Svitolina battled back to defeat Yanina Wickmayer, 4-6, 6-3, 6-4. No.15 seed Sara Errani wasn't able to pull off the same Houdini act against the always dangerous Camila Giorgi, losing, 7-5, 7-5, to her countrywoman in one hour and 37 minutes. Ekaterina Makarova reunited with former doubles partner Elena Vesnina for the first time since Wimbledon, and put down a comprehensive 6-3, 6-4 singles win over Annika Beck; Christina McHale was equally emphatic over Anna-Lena Friedsam, 6-0, 6-4.
In doubles, No.5 seeds Caroline Garcia and Kristina Mladenovic won a 10th straight match in their first round over Anna-Lena Groenefeld and CoCo Vandeweghe, winning, 6-4, 7-5. Including their decisive Fed Cup win over the Netherlands, Garcia and Mladenovic haven't lost a match since Miami, taking home titles in Charleston and Stuttgart - where they took out top seeds and Co-No.1s Martina Hingis and Sania Mirza - in back to back weeks. No.7 seeds Carla Suárez Navarro and Garbiñe Muguruza thrilled the home crowd with a 6-4, 7-6(4) win over Gabriela Dabrowski and Anastasia Rodionova, while Xu Yi-Fan and Zheng Saisai were three games into their first rounder with Kasatkina and Laura Siegemund when the Stuttgart runner-up was forced to retire due to dizziness.