The top-seeded Wozniacki did not give Ayumi Morita of Japan a single break opportunity as the Danish player rolled to a 6-2, 6-3 win at the clay-court event.
The eighth-seeded Sharapova won on her second match point when Rus netted a forehand.
After dropping the first set, Sharapova broke Rus three times in the second set. Sharapova then forced Rus from corner to corner with powerful groundstrokes as the Dutch player was eventually overwhelmed.
Arantxa Parra Santonja ousted former top 10 player Flavia Pennetta of Italy 6-3, 7-5 as the unseeded Spanish challenger hit eight aces on her way to saving eight break points and breaking her opponent's serve four times.
In other upsets, Sara Errani of Italy ousted sixth-seeded Klara Zakopalova 7-6 (4), 6-4 while American Bethanie Mattek-Sands rallied to beat 15th-seeded Ana Ivanovic of Serbia 0-6, 6-4, 6-4.
Third-seeded Francesca Schiavone of Italy beat Peng Shuai of China 7-5, 7-6 (2), while 14th-seeded Julia Goerges rallied to win 6-7 (3), 6-1, 6-4 against Kaia Kanepi.
11th-seeded Marion Bartoli of France shook off Simona Halep of Romania to win 6-4, 6-1.
Slovakia's Daniela Hantuchova, Sofia Arvidsson of Sweden and Russians Ekaterina Makarova and Elena Vesnina also won.