Seventh-seed Peng, runner up in this International clay-court event in 2006, went down 6-4 4-6 6-2 to Silvia Soler-Espinosa, while Riske was beaten 6-4 6-4 by Madison Keys.
After both players struggled to hold their serve in the early stages, Soler-Espinosa forged ahead after a crucial break in game nine.
The Chinese pulled herself level with a break of her own in game 10 of the second, but the Spaniard raced to a 4-0 lead in the decider and held her nerve to progress to the last eight.
Riske, meanwhile, was dislodged by American Keys, who took the lead with a break in game 10 of the first set.
Eighth-seed Riske fell 5-3 behind in set two and, although she broke back immediately, lost her serve once more in the very next game and was sent spinning out.
Soler-Espinosa will now take on Camila Giorgi, came from a set down to beat Claire Feuerstein 5-7 7-5 7-6 (7-2), while Keys will come up against Julia Goerges, conqueror of number one seed Sloane Stephens in round one.
Goerges followed up that success on Wednesday by seeing off Lauren Davis 7-5 6-4.
Petkovic, the number four seed and champion here three years ago, had little trouble in easing past Vania King, breaking her opponent five times on the way to a 6-3 6-2 success.
That win earned her a quarter-final clash with Monica Puig, who needed just 66 minutes to get the better of Mirjana Lucic, 6-3 6-1.
Elsewhere, Zarina Diyas beat Ajla Tomjanovic 6-4 7-6 (7-4), and will now face Christina McHale, who came through against Casey Dellacqua 6-3 7-5.