On Friday, Siegemund will face top-ranked Serena Williams, and Nara will play 10th-seeded Venus Williams.
Nara beat Teliana Pereira of Brazil 6-1, 6-2, and Siegemund topped Irina-Camelia Begu of Romania 3-6, 6-4, 6-4. At No. 35, Begu was the highest-ranked player in action on the opening day with all 32 seeds receiving first-round byes.
The other over 30s fared better, with No. 36 Lesia Tsurenko, No. 37 Barbora Strycova and No. 38 Coco Vandweghe all posting straight-set wins. Tsurenko, from the Ukraine, beat Timea Babos of Hungary 7-5, 6-4; Strycova, from the Czech Republic, rolled over Aliaksandra Sasnovich of Belarus, 6-1, 6-3; and Vandeweghe, who makes her home in Southern California, was a 6-4, 6-4 winner over Kiki Bertens of the Netherlands.
British wild-card Heather Watson rallied from a 5-1 deficit in the first set to beat Galina Voskoboeva of Kazakhstan 7-6 (4), 4-6, 6-1.
Americans Alison Riske and Irina Falconi dropped out. Lucie Hradecka of the Czech Republic beat Riske 7-6 (4), 6-2, and Carina Witthoeft of Germany came back to top Falconi 0-6, 6-4, 6-4.