The American, whose two previous last-eight appearances were also at the Aegon Classic, needed just 54 minutes to oust the Russian, who had shocked British number two Heather Watson in the previous round.
Riske, who like Kudryavtseva is a qualifier for this tournament, lost just 14 points on serve and managed two breaks in each set.
Her fellow American Madison Keys also progressed with an impressive 6-3 6-2 win over sixth seed Mona Barthel of Germany.
"No match on grass is easy because things can change so quickly, but I was really happy I was able to get on and get off," Keys said.
"I think I was really solid off the baseline today, which really helped me play some good return games and break her. And I also served really well today."
WTA Edgbaston Round 3 results:
16-Magdalena Rybarikova (Slovakia) beat 1-Kirsten Flipkens (Belgium) 7-6(5) 6-2
3-Sorana Cirstea (Romania) beat 13-Bojana Jovanovski (Serbia) 6-1 1-6 6-1
5-Sabine Lisicki (Germany) beat Mirjana Lucic-Baroni (Croatia) 7-5 2-6 6-4
Madison Keys (U.S.) beat 6-Mona Barthel (Germany) 6-3 6-2
Daniela Hantuchova (Slovakia) beat 12-Kristina Mladenovic (France) 3-6 7-6(6) 6-4
15-Francesca Schiavone (Italy) beat Marina Erakovic (New Zealand) 7-6(3) 6-3
Alison Riske (U.S.) beat Alla Kudryavtseva (Russia) 6-1 6-2
Donna Vekic (Croatia) beat Maria Sanchez (U.S.) 4-6 6-2 6-2
WTA Nuremberg quarter-final results:
1-Jelena Jankovic (Serbia) beat 6-Lourdes Dominguez Lino (Spain) 6-4 6-0
Andrea Petkovic (Germany) beat 8-Annika Beck (Germany) 4-6 6-3 7-5
5-Lucie Safarova (Czech Republic) beat Polona Hercog (Slovenia) 7-6(5) 3-6 6-4
7-Simona Halep (Romania) beat Galina Voskoboeva (Kazakhstan) 6-4 6-1