Cirstea rallied to upset fourth-seeded Anastasia Pavlyuchenkova of Russia 4-6, 6-0, 6-4 and Rodina ousted No. 6 Julia Goerges of Germany 6-3, 6-4. Rodionova advanced without playing because No. 9 Flavia Pennetta of Italy pulled out with a left thigh injury.
Rodina, who is ranked 104th, lost in the qualifier but entered the main draw when Germany's Andrea Petkovic pulled out with a knee injury.
Rodina held serve throughout and dominated play against the 21st-ranked Goerges with strong ground strokes.
The 15th-ranked Pavlyuchenkova had 11 double faults and lost eight straight games against Cirstea after winning the opening set. Trailing 2-0 in the decider, she broke back but dropped serve two more times.
In her second quarterfinal of the season, Cirstea will play either Lucie Safarova or Brianti.
Earlier Wednesday, Pennetta was a 7-6 (4), 6-2 winner against Elena Vesnina before withdrawing from her second-round match against Rodionova, who beat Barbora Zahlavova Strycova of the Czech Republic 7-6 (6), 6-1.
Patricia Mayr-Achleitner recovered from losing the opening set to beat Stephanie Foretz Gacon of France 3-6, 6-2, 6-2. The Austrian next takes on top-seeded Wimbledon champion Petra Kvitova for a place in the quarterfinals.
Former champion Daniela Hantuchova missed a match point in the second set tiebreaker but still held off Petra Martic of Croatia 6-3, 6-7 (6), 6-1. Martic had her right thigh muscle taped after winning the second set and seemed to be hampered by the injury in the decider.