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.
Notable deaths of 2014 [PHOTOS]