Riske, a 22-year-old Pittsburgh native, rallied for a 2-6, 6-2, 6-3 victory over grass-court specialist Paszek, who has advanced to the Wimbledon quarterfinals the last two years.
In another Round 2 match-up, No. 6 Mona Barthel of Germany held off Serbia's Vesna Dolonc 7-5, 2-6, 7-5, but eighth-seeded Pole Urszula Radwanska was bounced by Croatia's Donna Vekic 6-3, 6-2.
Madison Keys also gained the third round with a comeback 2-6, 6-3, 7-6 (7-3) decision over fellow unseeded American Jamie Hampton.
Elsewhere at Edgbaston Priory Club Tuesday, first-round contests saw No. 9 Yanina Wickmayer of Belgium, No. 12 Kristina Mladenovic of France, No. 14 Heather Watson of Britain, No. 15 Francesca Schiavone of Italy and Slovakian Daniela Hantuchova emerge with victories.