Azarenka beat Svetlana Kuznetsova of Russia 7-6 (5), 6-4 in a tough opening match.
The Australian Open champion and Kuznetsova traded breaks in the first set. Just when it looked as if the second set was going to end in another tiebreaker, Azarenka broke again to close out the match.
"It was a really close match, so I was just happy that I won because they were difficult games to break," said Azarenka, who added that the differences between the new surface and traditional red clay were not limited to color.
"It is pretty slippery. The bounce is different which changes everything completely already. It's just a completely different thing."
Sharapova had an easier debut with a comfortable 6-0, 6-3 victory over Irina-Camelia Begu.
Sharapova stormed to an early lead by winning the first seven games. After Begu saved a match point the Romanian player had a double break chance, but Sharapova saved both points to hold serve and secure a second-round meeting with Klara Zakopalova.
Fourth-seeded Agnieszka Radwanska didn't give up a single break chance in her 6-3, 6-1 win over Lara Arruabarrena-Veci.